Continuity of nonlinear eigenvalues in CD(K,∞) spaces with respect to measured Gromov–Hausdorff convergence View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-04

AUTHORS

Luigi Ambrosio, Shouhei Honda, Jacobus W. Portegies

ABSTRACT

In this note we prove in the nonlinear setting of CD(K,∞) spaces the stability of the Krasnoselskii spectrum of the Laplace operator -Δ under measured Gromov–Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of CD∗(K,N) metric measure spaces with uniformly bounded diameter. Additionally, we show that every element λ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial u satisfying the eigenvalue equation -Δu=λu. More... »

PAGES

34

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00526-018-1315-0

DOI

http://dx.doi.org/10.1007/s00526-018-1315-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1100992290


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": "Scuola Normale Superiore di Pisa", 
          "id": "https://www.grid.ac/institutes/grid.6093.c", 
          "name": [
            "Scuola Normale Superiore, Pisa, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ambrosio", 
        "givenName": "Luigi", 
        "id": "sg:person.012621721115.68", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Tohoku University", 
          "id": "https://www.grid.ac/institutes/grid.69566.3a", 
          "name": [
            "Tohoku University, Sendai, Japan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Honda", 
        "givenName": "Shouhei", 
        "id": "sg:person.016457223325.07", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016457223325.07"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Eindhoven University of Technology", 
          "id": "https://www.grid.ac/institutes/grid.6852.9", 
          "name": [
            "Eindhoven University, Eindhoven, Netherlands"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Portegies", 
        "givenName": "Jacobus W.", 
        "id": "sg:person.015530336103.78", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015530336103.78"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/978-94-011-5282-2_12", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000037752", 
          "https://doi.org/10.1007/978-94-011-5282-2_12"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-011-5282-2_12", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1000037752", 
          "https://doi.org/10.1007/978-94-011-5282-2_12"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2010.03.024", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004423076"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.anihpb.2005.12.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1004740148"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00222-013-0456-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005998425", 
          "https://doi.org/10.1007/s00222-013-0456-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00526-011-0442-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006224392", 
          "https://doi.org/10.1007/s00526-011-0442-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11511-006-0003-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008600697", 
          "https://doi.org/10.1007/s11511-006-0003-7"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11511-006-0002-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1009828547", 
          "https://doi.org/10.1007/s11511-006-0002-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf01389241", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022704548", 
          "https://doi.org/10.1007/bf01389241"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2016.10.030", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032549738"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1112/plms/pdv047", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039507548"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bfb0081739", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051383692", 
          "https://doi.org/10.1007/bfb0081739"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/memo/1113", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1059344070"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1215/00127094-2681605", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064411389"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1216/rmj-1973-3-2-161", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064427470"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/crelle-2013-0061", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1067527944"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4007/annals.2009.169.903", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071867138"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0294-1449(16)30348-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084044575"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/jdg/1214342146", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1084458704"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/9783110550832", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1095899664"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1515/9781400856459", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1096908736"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-04", 
    "datePublishedReg": "2018-04-01", 
    "description": "In this note we prove in the nonlinear setting of CD(K,\u221e) spaces the stability of the Krasnoselskii spectrum of the Laplace operator -\u0394 under measured Gromov\u2013Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of CD\u2217(K,N) metric measure spaces with uniformly bounded diameter. Additionally, we show that every element \u03bb in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial u satisfying the eigenvalue equation -\u0394u=\u03bbu.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00526-018-1315-0", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.5917132", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1043284", 
        "issn": [
          "0944-2669", 
          "1432-0835"
        ], 
        "name": "Calculus of Variations and Partial Differential Equations", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "57"
      }
    ], 
    "name": "Continuity of nonlinear eigenvalues in CD(K,\u221e) spaces with respect to measured Gromov\u2013Hausdorff convergence", 
    "pagination": "34", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "2b6e13124660c199b23fb65faf9d539718e80a4089cb56a8f22e76113b4d019e"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00526-018-1315-0"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1100992290"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00526-018-1315-0", 
      "https://app.dimensions.ai/details/publication/pub.1100992290"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-10T14:02", 
    "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/v90/0000000001_0000000264/records_8660_00000484.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007/s00526-018-1315-0"
  }
]
 

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/s00526-018-1315-0'

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/s00526-018-1315-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00526-018-1315-0'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00526-018-1315-0'


 

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

150 TRIPLES      21 PREDICATES      47 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00526-018-1315-0 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N6fe40dd5d52a4d99bede95a41611cc5b
4 schema:citation sg:pub.10.1007/978-94-011-5282-2_12
5 sg:pub.10.1007/bf01389241
6 sg:pub.10.1007/bfb0081739
7 sg:pub.10.1007/s00222-013-0456-1
8 sg:pub.10.1007/s00526-011-0442-7
9 sg:pub.10.1007/s11511-006-0002-8
10 sg:pub.10.1007/s11511-006-0003-7
11 https://doi.org/10.1016/j.anihpb.2005.12.001
12 https://doi.org/10.1016/j.jfa.2010.03.024
13 https://doi.org/10.1016/j.jfa.2016.10.030
14 https://doi.org/10.1016/s0294-1449(16)30348-1
15 https://doi.org/10.1090/memo/1113
16 https://doi.org/10.1112/plms/pdv047
17 https://doi.org/10.1215/00127094-2681605
18 https://doi.org/10.1216/rmj-1973-3-2-161
19 https://doi.org/10.1515/9781400856459
20 https://doi.org/10.1515/9783110550832
21 https://doi.org/10.1515/crelle-2013-0061
22 https://doi.org/10.4007/annals.2009.169.903
23 https://doi.org/10.4310/jdg/1214342146
24 schema:datePublished 2018-04
25 schema:datePublishedReg 2018-04-01
26 schema:description In this note we prove in the nonlinear setting of CD(K,∞) spaces the stability of the Krasnoselskii spectrum of the Laplace operator -Δ under measured Gromov–Hausdorff convergence, under an additional compactness assumption satisfied, for instance, by sequences of CD∗(K,N) metric measure spaces with uniformly bounded diameter. Additionally, we show that every element λ in the Krasnoselskii spectrum is indeed an eigenvalue, namely there exists a nontrivial u satisfying the eigenvalue equation -Δu=λu.
27 schema:genre research_article
28 schema:inLanguage en
29 schema:isAccessibleForFree false
30 schema:isPartOf N2a918e692da34d81b378c40095024785
31 N64e9b9e879e447489fd698e7233b1f41
32 sg:journal.1043284
33 schema:name Continuity of nonlinear eigenvalues in CD(K,∞) spaces with respect to measured Gromov–Hausdorff convergence
34 schema:pagination 34
35 schema:productId N81211535b81b417c899bc5bacbc1b1db
36 Na68b3655227a4975b36b535526875b77
37 Nc584d7f3f1bf4afba46f6651b9f52f23
38 schema:sameAs https://app.dimensions.ai/details/publication/pub.1100992290
39 https://doi.org/10.1007/s00526-018-1315-0
40 schema:sdDatePublished 2019-04-10T14:02
41 schema:sdLicense https://scigraph.springernature.com/explorer/license/
42 schema:sdPublisher N63ddeff563364eeeb412178b9e05e721
43 schema:url http://link.springer.com/10.1007/s00526-018-1315-0
44 sgo:license sg:explorer/license/
45 sgo:sdDataset articles
46 rdf:type schema:ScholarlyArticle
47 N2a918e692da34d81b378c40095024785 schema:issueNumber 2
48 rdf:type schema:PublicationIssue
49 N63ddeff563364eeeb412178b9e05e721 schema:name Springer Nature - SN SciGraph project
50 rdf:type schema:Organization
51 N64e9b9e879e447489fd698e7233b1f41 schema:volumeNumber 57
52 rdf:type schema:PublicationVolume
53 N6fe40dd5d52a4d99bede95a41611cc5b rdf:first sg:person.012621721115.68
54 rdf:rest Nafe7b693b82a448e8782f832a22f4934
55 N81211535b81b417c899bc5bacbc1b1db schema:name readcube_id
56 schema:value 2b6e13124660c199b23fb65faf9d539718e80a4089cb56a8f22e76113b4d019e
57 rdf:type schema:PropertyValue
58 N8af4e8a9e1dd47f59ea093d48aa77352 rdf:first sg:person.015530336103.78
59 rdf:rest rdf:nil
60 Na68b3655227a4975b36b535526875b77 schema:name doi
61 schema:value 10.1007/s00526-018-1315-0
62 rdf:type schema:PropertyValue
63 Nafe7b693b82a448e8782f832a22f4934 rdf:first sg:person.016457223325.07
64 rdf:rest N8af4e8a9e1dd47f59ea093d48aa77352
65 Nc584d7f3f1bf4afba46f6651b9f52f23 schema:name dimensions_id
66 schema:value pub.1100992290
67 rdf:type schema:PropertyValue
68 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
69 schema:name Mathematical Sciences
70 rdf:type schema:DefinedTerm
71 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
72 schema:name Pure Mathematics
73 rdf:type schema:DefinedTerm
74 sg:grant.5917132 http://pending.schema.org/fundedItem sg:pub.10.1007/s00526-018-1315-0
75 rdf:type schema:MonetaryGrant
76 sg:journal.1043284 schema:issn 0944-2669
77 1432-0835
78 schema:name Calculus of Variations and Partial Differential Equations
79 rdf:type schema:Periodical
80 sg:person.012621721115.68 schema:affiliation https://www.grid.ac/institutes/grid.6093.c
81 schema:familyName Ambrosio
82 schema:givenName Luigi
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012621721115.68
84 rdf:type schema:Person
85 sg:person.015530336103.78 schema:affiliation https://www.grid.ac/institutes/grid.6852.9
86 schema:familyName Portegies
87 schema:givenName Jacobus W.
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.015530336103.78
89 rdf:type schema:Person
90 sg:person.016457223325.07 schema:affiliation https://www.grid.ac/institutes/grid.69566.3a
91 schema:familyName Honda
92 schema:givenName Shouhei
93 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016457223325.07
94 rdf:type schema:Person
95 sg:pub.10.1007/978-94-011-5282-2_12 schema:sameAs https://app.dimensions.ai/details/publication/pub.1000037752
96 https://doi.org/10.1007/978-94-011-5282-2_12
97 rdf:type schema:CreativeWork
98 sg:pub.10.1007/bf01389241 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022704548
99 https://doi.org/10.1007/bf01389241
100 rdf:type schema:CreativeWork
101 sg:pub.10.1007/bfb0081739 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051383692
102 https://doi.org/10.1007/bfb0081739
103 rdf:type schema:CreativeWork
104 sg:pub.10.1007/s00222-013-0456-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005998425
105 https://doi.org/10.1007/s00222-013-0456-1
106 rdf:type schema:CreativeWork
107 sg:pub.10.1007/s00526-011-0442-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006224392
108 https://doi.org/10.1007/s00526-011-0442-7
109 rdf:type schema:CreativeWork
110 sg:pub.10.1007/s11511-006-0002-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1009828547
111 https://doi.org/10.1007/s11511-006-0002-8
112 rdf:type schema:CreativeWork
113 sg:pub.10.1007/s11511-006-0003-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008600697
114 https://doi.org/10.1007/s11511-006-0003-7
115 rdf:type schema:CreativeWork
116 https://doi.org/10.1016/j.anihpb.2005.12.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004740148
117 rdf:type schema:CreativeWork
118 https://doi.org/10.1016/j.jfa.2010.03.024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1004423076
119 rdf:type schema:CreativeWork
120 https://doi.org/10.1016/j.jfa.2016.10.030 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032549738
121 rdf:type schema:CreativeWork
122 https://doi.org/10.1016/s0294-1449(16)30348-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084044575
123 rdf:type schema:CreativeWork
124 https://doi.org/10.1090/memo/1113 schema:sameAs https://app.dimensions.ai/details/publication/pub.1059344070
125 rdf:type schema:CreativeWork
126 https://doi.org/10.1112/plms/pdv047 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039507548
127 rdf:type schema:CreativeWork
128 https://doi.org/10.1215/00127094-2681605 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064411389
129 rdf:type schema:CreativeWork
130 https://doi.org/10.1216/rmj-1973-3-2-161 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064427470
131 rdf:type schema:CreativeWork
132 https://doi.org/10.1515/9781400856459 schema:sameAs https://app.dimensions.ai/details/publication/pub.1096908736
133 rdf:type schema:CreativeWork
134 https://doi.org/10.1515/9783110550832 schema:sameAs https://app.dimensions.ai/details/publication/pub.1095899664
135 rdf:type schema:CreativeWork
136 https://doi.org/10.1515/crelle-2013-0061 schema:sameAs https://app.dimensions.ai/details/publication/pub.1067527944
137 rdf:type schema:CreativeWork
138 https://doi.org/10.4007/annals.2009.169.903 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071867138
139 rdf:type schema:CreativeWork
140 https://doi.org/10.4310/jdg/1214342146 schema:sameAs https://app.dimensions.ai/details/publication/pub.1084458704
141 rdf:type schema:CreativeWork
142 https://www.grid.ac/institutes/grid.6093.c schema:alternateName Scuola Normale Superiore di Pisa
143 schema:name Scuola Normale Superiore, Pisa, Italy
144 rdf:type schema:Organization
145 https://www.grid.ac/institutes/grid.6852.9 schema:alternateName Eindhoven University of Technology
146 schema:name Eindhoven University, Eindhoven, Netherlands
147 rdf:type schema:Organization
148 https://www.grid.ac/institutes/grid.69566.3a schema:alternateName Tohoku University
149 schema:name Tohoku University, Sendai, Japan
150 rdf:type schema:Organization
 




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


...