A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2019-04

AUTHORS

Xiaobao Zhu

ABSTRACT

In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularity. Precisely, let (Σ,D) be such a surface with divisor D=Σi=1mβipi, where βi > −1 and pi ∈ Σ for i = 1, …, m, and g be a metric representing D. Denote b0 = 4π(1 + min1⩽i⩽mβi). Suppose ψ : Σ → ℝ is a continuous function with ∫Σψdvg ≠ 0 and define λ1∗∗(∑,g)=infu∈H1(∑,g),∫∑ψudvg=0,∫∑u2dvg=1∫∑|∇gu|2dvg. Then for anyα∈[0,λ1**(Σ,g)), we have supu∈H1(∑,g),∫∑ψu=0,∫∑|∇gu|2dvg−α∫∑u2dvg⩽1∫∑eb0u2dvg<+∞. When b > b0, the integrals ∫∑ebu2dvg are still finite, but the supremum is infinity. Moreover, we prove that the extremal function for the above inequality exists. More... »

PAGES

699-718

References to SciGraph publications

  • 2016-10. A Trudinger–Moser Inequality on a Compact Riemannian Surface Involving Gaussian Curvature in THE JOURNAL OF GEOMETRIC ANALYSIS
  • 2007-07. A singular Moser-Trudinger embedding and its applications in NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS NODEA
  • 1993-12. Sharp borderline Sobolev inequalities on compact Riemannian manifolds in COMMENTARII MATHEMATICI HELVETICI
  • 2005-05. Extremal functions for the Moser-Trudinger inequalities on compact Riemannian manifolds in SCIENCE IN CHINA SERIES A MATHEMATICS
  • 1992-12. Extremal functions for the trudinger-moser inequality in 2 dimensions in COMMENTARII MATHEMATICI HELVETICI
  • 2015-10. Extremal functions for the singular Moser-Trudinger inequality in 2 dimensions in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
  • 2018-06. Existence of solutions to a class of Kazdan-Warner equations on compact Riemannian surface in SCIENCE CHINA MATHEMATICS
  • Journal

    TITLE

    Science China Mathematics

    ISSUE

    4

    VOLUME

    62

    Author Affiliations

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s11425-017-9174-2

    DOI

    http://dx.doi.org/10.1007/s11425-017-9174-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1101359220


    Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
    Incoming Citations Browse incoming citations for this publication using opencitations.net

    JSON-LD is the canonical representation for SciGraph data.

    TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

    [
      {
        "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
        "about": [
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0101", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Pure Mathematics", 
            "type": "DefinedTerm"
          }, 
          {
            "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
            "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
            "name": "Mathematical Sciences", 
            "type": "DefinedTerm"
          }
        ], 
        "author": [
          {
            "affiliation": {
              "alternateName": "Renmin University of China", 
              "id": "https://www.grid.ac/institutes/grid.24539.39", 
              "name": [
                "Department of Mathematics, Renmin University of China, 100872, Beijing, China"
              ], 
              "type": "Organization"
            }, 
            "familyName": "Zhu", 
            "givenName": "Xiaobao", 
            "id": "sg:person.011774134325.44", 
            "sameAs": [
              "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011774134325.44"
            ], 
            "type": "Person"
          }
        ], 
        "citation": [
          {
            "id": "sg:pub.10.1007/s00030-006-4025-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1003796656", 
              "https://doi.org/10.1007/s00030-006-4025-9"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1081/pde-120028854", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1010431327"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s12220-015-9653-z", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1013738374", 
              "https://doi.org/10.1007/s12220-015-9653-z"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2006.06.002", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1019945322"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02566514", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1021298223", 
              "https://doi.org/10.1007/bf02566514"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2016.12.028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024032811"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2016.12.028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024032811"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2016.12.028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024032811"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2016.12.028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024032811"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-1991-1005085-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1024934268"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02565828", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025871983", 
              "https://doi.org/10.1007/bf02565828"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/bf02565828", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1025871983", 
              "https://doi.org/10.1007/bf02565828"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-96-01541-3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1032500648"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jfa.2013.09.009", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1037163701"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jde.2015.01.004", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1038970824"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9939-1990-0990415-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1043660819"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s00526-015-0867-5", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1049202826", 
              "https://doi.org/10.1007/s00526-015-0867-5"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1090/s0002-9947-07-04272-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1051072638"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0308210500001219", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054892361"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1017/s0308210500001219", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1054892361"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1093/imrn/rnp194", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059690550"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1093/imrn/rnp194", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1059690550"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-91-06325-8", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064419695"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1215/s0012-7094-95-07821-1", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1064420089"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1360/04ys0050", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1065069583", 
              "https://doi.org/10.1360/04ys0050"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1512/iumj.1968.17.17028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1067510947"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcds.2009.25.963", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071733935"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.3934/dcds.2014.34.2617", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1071734952"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4171/rmi/6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072320923"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.4310/ajm.1997.v1.n2.a3", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1072456179"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.5802/aif.232", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1073138098"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/s0294-1449(16)30338-9", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084044565"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2017.02.029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084097899"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2017.02.029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084097899"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2017.02.029", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1084097899"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "sg:pub.10.1007/s11425-017-9086-6", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1093029654", 
              "https://doi.org/10.1007/s11425-017-9086-6"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.na.2017.12.001", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1099927641"
            ], 
            "type": "CreativeWork"
          }, 
          {
            "id": "https://doi.org/10.1016/j.jde.2017.12.028", 
            "sameAs": [
              "https://app.dimensions.ai/details/publication/pub.1100155108"
            ], 
            "type": "CreativeWork"
          }
        ], 
        "datePublished": "2019-04", 
        "datePublishedReg": "2019-04-01", 
        "description": "In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularity. Precisely, let (\u03a3,D) be such a surface with divisor D=\u03a3i=1m\u03b2ipi, where \u03b2i > \u22121 and pi \u2208 \u03a3 for i = 1, \u2026, m, and g be a metric representing D. Denote b0 = 4\u03c0(1 + min1\u2a7di\u2a7dm\u03b2i). Suppose \u03c8 : \u03a3 \u2192 \u211d is a continuous function with \u222b\u03a3\u03c8dvg \u2260 0 and define \u03bb1\u2217\u2217(\u2211,g)=infu\u2208H1(\u2211,g),\u222b\u2211\u03c8udvg=0,\u222b\u2211u2dvg=1\u222b\u2211|\u2207gu|2dvg. Then for any\u03b1\u2208[0,\u03bb1**(\u03a3,g)), we have supu\u2208H1(\u2211,g),\u222b\u2211\u03c8u=0,\u222b\u2211|\u2207gu|2dvg\u2212\u03b1\u222b\u2211u2dvg\u2a7d1\u222b\u2211eb0u2dvg<+\u221e. When b > b0, the integrals \u222b\u2211ebu2dvg are still finite, but the supremum is infinity. Moreover, we prove that the extremal function for the above inequality exists.", 
        "genre": "research_article", 
        "id": "sg:pub.10.1007/s11425-017-9174-2", 
        "inLanguage": [
          "en"
        ], 
        "isAccessibleForFree": false, 
        "isPartOf": [
          {
            "id": "sg:journal.1048022", 
            "issn": [
              "1674-7283", 
              "1869-1862"
            ], 
            "name": "Science China Mathematics", 
            "type": "Periodical"
          }, 
          {
            "issueNumber": "4", 
            "type": "PublicationIssue"
          }, 
          {
            "type": "PublicationVolume", 
            "volumeNumber": "62"
          }
        ], 
        "name": "A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities", 
        "pagination": "699-718", 
        "productId": [
          {
            "name": "readcube_id", 
            "type": "PropertyValue", 
            "value": [
              "614e2913a58e31ee341ce72314035efeb50e3541a9e72e1f4cb748ceebc66c94"
            ]
          }, 
          {
            "name": "doi", 
            "type": "PropertyValue", 
            "value": [
              "10.1007/s11425-017-9174-2"
            ]
          }, 
          {
            "name": "dimensions_id", 
            "type": "PropertyValue", 
            "value": [
              "pub.1101359220"
            ]
          }
        ], 
        "sameAs": [
          "https://doi.org/10.1007/s11425-017-9174-2", 
          "https://app.dimensions.ai/details/publication/pub.1101359220"
        ], 
        "sdDataset": "articles", 
        "sdDatePublished": "2019-04-11T12:54", 
        "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
        "sdPublisher": {
          "name": "Springer Nature - SN SciGraph project", 
          "type": "Organization"
        }, 
        "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000364_0000000364/records_72865_00000001.jsonl", 
        "type": "ScholarlyArticle", 
        "url": "https://link.springer.com/10.1007%2Fs11425-017-9174-2"
      }
    ]
     

    Download the RDF metadata as:  json-ld nt turtle xml License info

    HOW TO GET THIS DATA PROGRAMMATICALLY:

    JSON-LD is a popular format for linked data which is fully compatible with JSON.

    curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s11425-017-9174-2'

    N-Triples is a line-based linked data format ideal for batch operations.

    curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s11425-017-9174-2'

    Turtle is a human-readable linked data format.

    curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11425-017-9174-2'

    RDF/XML is a standard XML format for linked data.

    curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11425-017-9174-2'


     

    This table displays all metadata directly associated to this object as RDF triples.

    158 TRIPLES      21 PREDICATES      57 URIs      19 LITERALS      7 BLANK NODES

    Subject Predicate Object
    1 sg:pub.10.1007/s11425-017-9174-2 schema:about anzsrc-for:01
    2 anzsrc-for:0101
    3 schema:author N44146d97d7b64098b1db1af8a1f791a2
    4 schema:citation sg:pub.10.1007/bf02565828
    5 sg:pub.10.1007/bf02566514
    6 sg:pub.10.1007/s00030-006-4025-9
    7 sg:pub.10.1007/s00526-015-0867-5
    8 sg:pub.10.1007/s11425-017-9086-6
    9 sg:pub.10.1007/s12220-015-9653-z
    10 sg:pub.10.1360/04ys0050
    11 https://doi.org/10.1016/j.jde.2015.01.004
    12 https://doi.org/10.1016/j.jde.2017.12.028
    13 https://doi.org/10.1016/j.jfa.2006.06.002
    14 https://doi.org/10.1016/j.jfa.2013.09.009
    15 https://doi.org/10.1016/j.jfa.2016.12.028
    16 https://doi.org/10.1016/j.na.2017.02.029
    17 https://doi.org/10.1016/j.na.2017.12.001
    18 https://doi.org/10.1016/s0294-1449(16)30338-9
    19 https://doi.org/10.1017/s0308210500001219
    20 https://doi.org/10.1081/pde-120028854
    21 https://doi.org/10.1090/s0002-9939-1990-0990415-9
    22 https://doi.org/10.1090/s0002-9947-07-04272-9
    23 https://doi.org/10.1090/s0002-9947-1991-1005085-9
    24 https://doi.org/10.1090/s0002-9947-96-01541-3
    25 https://doi.org/10.1093/imrn/rnp194
    26 https://doi.org/10.1215/s0012-7094-91-06325-8
    27 https://doi.org/10.1215/s0012-7094-95-07821-1
    28 https://doi.org/10.1512/iumj.1968.17.17028
    29 https://doi.org/10.3934/dcds.2009.25.963
    30 https://doi.org/10.3934/dcds.2014.34.2617
    31 https://doi.org/10.4171/rmi/6
    32 https://doi.org/10.4310/ajm.1997.v1.n2.a3
    33 https://doi.org/10.5802/aif.232
    34 schema:datePublished 2019-04
    35 schema:datePublishedReg 2019-04-01
    36 schema:description In this paper, using the method of blow-up analysis, we establish a generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularity. Precisely, let (Σ,D) be such a surface with divisor D=Σi=1mβipi, where βi > −1 and pi ∈ Σ for i = 1, …, m, and g be a metric representing D. Denote b0 = 4π(1 + min1⩽i⩽mβi). Suppose ψ : Σ → ℝ is a continuous function with ∫Σψdvg ≠ 0 and define λ1∗∗(∑,g)=infu∈H1(∑,g),∫∑ψudvg=0,∫∑u2dvg=1∫∑|∇gu|2dvg. Then for anyα∈[0,λ1**(Σ,g)), we have supu∈H1(∑,g),∫∑ψu=0,∫∑|∇gu|2dvg−α∫∑u2dvg⩽1∫∑eb0u2dvg<+∞. When b > b0, the integrals ∫∑ebu2dvg are still finite, but the supremum is infinity. Moreover, we prove that the extremal function for the above inequality exists.
    37 schema:genre research_article
    38 schema:inLanguage en
    39 schema:isAccessibleForFree false
    40 schema:isPartOf N70ef4883bc064376abe5df1d28ffa553
    41 Nd5ee58f302e84dbebe28f1ff735d2e8b
    42 sg:journal.1048022
    43 schema:name A generalized Trudinger-Moser inequality on a compact Riemannian surface with conical singularities
    44 schema:pagination 699-718
    45 schema:productId Nc0038c0d7aec4c1c8fc356516c6585d8
    46 Nf94dc98a38a54b46bdda469157f18039
    47 Nfcefce84a0484ebeba3368457a4f2f0f
    48 schema:sameAs https://app.dimensions.ai/details/publication/pub.1101359220
    49 https://doi.org/10.1007/s11425-017-9174-2
    50 schema:sdDatePublished 2019-04-11T12:54
    51 schema:sdLicense https://scigraph.springernature.com/explorer/license/
    52 schema:sdPublisher N93f8f32d7c3f4aea9228b74e0a2b4454
    53 schema:url https://link.springer.com/10.1007%2Fs11425-017-9174-2
    54 sgo:license sg:explorer/license/
    55 sgo:sdDataset articles
    56 rdf:type schema:ScholarlyArticle
    57 N44146d97d7b64098b1db1af8a1f791a2 rdf:first sg:person.011774134325.44
    58 rdf:rest rdf:nil
    59 N70ef4883bc064376abe5df1d28ffa553 schema:volumeNumber 62
    60 rdf:type schema:PublicationVolume
    61 N93f8f32d7c3f4aea9228b74e0a2b4454 schema:name Springer Nature - SN SciGraph project
    62 rdf:type schema:Organization
    63 Nc0038c0d7aec4c1c8fc356516c6585d8 schema:name doi
    64 schema:value 10.1007/s11425-017-9174-2
    65 rdf:type schema:PropertyValue
    66 Nd5ee58f302e84dbebe28f1ff735d2e8b schema:issueNumber 4
    67 rdf:type schema:PublicationIssue
    68 Nf94dc98a38a54b46bdda469157f18039 schema:name dimensions_id
    69 schema:value pub.1101359220
    70 rdf:type schema:PropertyValue
    71 Nfcefce84a0484ebeba3368457a4f2f0f schema:name readcube_id
    72 schema:value 614e2913a58e31ee341ce72314035efeb50e3541a9e72e1f4cb748ceebc66c94
    73 rdf:type schema:PropertyValue
    74 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
    75 schema:name Mathematical Sciences
    76 rdf:type schema:DefinedTerm
    77 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
    78 schema:name Pure Mathematics
    79 rdf:type schema:DefinedTerm
    80 sg:journal.1048022 schema:issn 1674-7283
    81 1869-1862
    82 schema:name Science China Mathematics
    83 rdf:type schema:Periodical
    84 sg:person.011774134325.44 schema:affiliation https://www.grid.ac/institutes/grid.24539.39
    85 schema:familyName Zhu
    86 schema:givenName Xiaobao
    87 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011774134325.44
    88 rdf:type schema:Person
    89 sg:pub.10.1007/bf02565828 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025871983
    90 https://doi.org/10.1007/bf02565828
    91 rdf:type schema:CreativeWork
    92 sg:pub.10.1007/bf02566514 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021298223
    93 https://doi.org/10.1007/bf02566514
    94 rdf:type schema:CreativeWork
    95 sg:pub.10.1007/s00030-006-4025-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003796656
    96 https://doi.org/10.1007/s00030-006-4025-9
    97 rdf:type schema:CreativeWork
    98 sg:pub.10.1007/s00526-015-0867-5 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049202826
    99 https://doi.org/10.1007/s00526-015-0867-5
    100 rdf:type schema:CreativeWork
    101 sg:pub.10.1007/s11425-017-9086-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1093029654
    102 https://doi.org/10.1007/s11425-017-9086-6
    103 rdf:type schema:CreativeWork
    104 sg:pub.10.1007/s12220-015-9653-z schema:sameAs https://app.dimensions.ai/details/publication/pub.1013738374
    105 https://doi.org/10.1007/s12220-015-9653-z
    106 rdf:type schema:CreativeWork
    107 sg:pub.10.1360/04ys0050 schema:sameAs https://app.dimensions.ai/details/publication/pub.1065069583
    108 https://doi.org/10.1360/04ys0050
    109 rdf:type schema:CreativeWork
    110 https://doi.org/10.1016/j.jde.2015.01.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038970824
    111 rdf:type schema:CreativeWork
    112 https://doi.org/10.1016/j.jde.2017.12.028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100155108
    113 rdf:type schema:CreativeWork
    114 https://doi.org/10.1016/j.jfa.2006.06.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019945322
    115 rdf:type schema:CreativeWork
    116 https://doi.org/10.1016/j.jfa.2013.09.009 schema:sameAs https://app.dimensions.ai/details/publication/pub.1037163701
    117 rdf:type schema:CreativeWork
    118 https://doi.org/10.1016/j.jfa.2016.12.028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024032811
    119 rdf:type schema:CreativeWork
    120 https://doi.org/10.1016/j.na.2017.02.029 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084097899
    121 rdf:type schema:CreativeWork
    122 https://doi.org/10.1016/j.na.2017.12.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1099927641
    123 rdf:type schema:CreativeWork
    124 https://doi.org/10.1016/s0294-1449(16)30338-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084044565
    125 rdf:type schema:CreativeWork
    126 https://doi.org/10.1017/s0308210500001219 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054892361
    127 rdf:type schema:CreativeWork
    128 https://doi.org/10.1081/pde-120028854 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010431327
    129 rdf:type schema:CreativeWork
    130 https://doi.org/10.1090/s0002-9939-1990-0990415-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043660819
    131 rdf:type schema:CreativeWork
    132 https://doi.org/10.1090/s0002-9947-07-04272-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051072638
    133 rdf:type schema:CreativeWork
    134 https://doi.org/10.1090/s0002-9947-1991-1005085-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024934268
    135 rdf:type schema:CreativeWork
    136 https://doi.org/10.1090/s0002-9947-96-01541-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032500648
    137 rdf:type schema:CreativeWork
    138 https://doi.org/10.1093/imrn/rnp194 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059690550
    139 rdf:type schema:CreativeWork
    140 https://doi.org/10.1215/s0012-7094-91-06325-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064419695
    141 rdf:type schema:CreativeWork
    142 https://doi.org/10.1215/s0012-7094-95-07821-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064420089
    143 rdf:type schema:CreativeWork
    144 https://doi.org/10.1512/iumj.1968.17.17028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067510947
    145 rdf:type schema:CreativeWork
    146 https://doi.org/10.3934/dcds.2009.25.963 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071733935
    147 rdf:type schema:CreativeWork
    148 https://doi.org/10.3934/dcds.2014.34.2617 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071734952
    149 rdf:type schema:CreativeWork
    150 https://doi.org/10.4171/rmi/6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072320923
    151 rdf:type schema:CreativeWork
    152 https://doi.org/10.4310/ajm.1997.v1.n2.a3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072456179
    153 rdf:type schema:CreativeWork
    154 https://doi.org/10.5802/aif.232 schema:sameAs https://app.dimensions.ai/details/publication/pub.1073138098
    155 rdf:type schema:CreativeWork
    156 https://www.grid.ac/institutes/grid.24539.39 schema:alternateName Renmin University of China
    157 schema:name Department of Mathematics, Renmin University of China, 100872, Beijing, China
    158 rdf:type schema:Organization
     




    Preview window. Press ESC to close (or click here)


    ...