Second commutation lemma for fractional H-measures View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2018-09

AUTHORS

Marko Erceg, Ivan Ivec

ABSTRACT

Classical H-measures introduced by Tartar (Proc R Soc Edinb 115A:193–230, 1990) and independently by Gérard (Commun Partial Differ Equ 16:1761–1794, 1991) are essentially suited for hyperbolic equations while parabolic equations fit in the framework of the parabolic H-measures developed by Antonić and Lazar (2007–2013). More recently the study of differential relations with fractional derivatives prompted the extension of the theory to arbitrary ratios, thus the fractional H-measures were introduced and applied to fractional conservation laws by Mitrović and Ivec (Commun Pure Appl Anal 10(6):1617–1627, 2011). In this paper we explore the transport property of fractional H-measures by studying fractional derivatives of commutators of multiplication and Fourier multiplier operators. In particular, we prove the Second commutation lemma suitable for fractional H-measures, comprehending the known hyperbolic and parabolic cases, while allowing for derivation of the corresponding propagation principle for fractional H-measures. At the end, on a model example we present this derivation of the transport equation for the fractional H-measure. More... »

PAGES

589-613

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s11868-017-0207-y

DOI

http://dx.doi.org/10.1007/s11868-017-0207-y

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1085073693


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": "International School for Advanced Studies", 
          "id": "https://www.grid.ac/institutes/grid.5970.b", 
          "name": [
            "Department of Mathematics, Faculty of Science, University of Zagreb, Bijeni\u010dka cesta 30, Zagreb, Croatia", 
            "Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste, Italy"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Erceg", 
        "givenName": "Marko", 
        "id": "sg:person.014772635175.37", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014772635175.37"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Zagreb", 
          "id": "https://www.grid.ac/institutes/grid.4808.4", 
          "name": [
            "Faculty of Metallurgy, University of Zagreb, Aleja narodnih heroja 3, Sisak, Croatia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Ivec", 
        "givenName": "Ivan", 
        "id": "sg:person.012334333661.49", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012334333661.49"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1016/j.jfa.2014.12.008", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002109903"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2014.12.008", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1002109903"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2013.06.006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1003062744"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03605309208820905", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005526371"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10958-009-9434-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005787696", 
          "https://doi.org/10.1007/s10958-009-9434-y"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s10958-009-9434-y", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005787696", 
          "https://doi.org/10.1007/s10958-009-9434-y"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/b138375", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008312238", 
          "https://doi.org/10.1007/b138375"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/b138375", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008312238", 
          "https://doi.org/10.1007/b138375"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jfa.2017.01.006", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010943305"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1080/03605309108820822", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1022528357"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmaa.2007.12.077", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025629115"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-49938-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025664356", 
          "https://doi.org/10.1007/978-3-540-49938-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-49938-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025664356", 
          "https://doi.org/10.1007/978-3-540-49938-1"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.camwa.2010.09.022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1028042753"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1155/2011/901084", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035722565"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.anihpc.2010.10.002", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035902472"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.nonrwa.2008.07.010", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1043410349"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00009-016-0699-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049531261", 
          "https://doi.org/10.1007/s00009-016-0699-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500020606", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054893743"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/s0308210500023325", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1054894015"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.3934/cpaa.2011.10.1617", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1071731755"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.4310/dpde.2012.v9.n3.a3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1072459723"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.2298/fil1716027e", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1101870230"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2018-09", 
    "datePublishedReg": "2018-09-01", 
    "description": "Classical H-measures introduced by Tartar (Proc R Soc Edinb 115A:193\u2013230, 1990) and independently by G\u00e9rard (Commun Partial Differ Equ 16:1761\u20131794, 1991) are essentially suited for hyperbolic equations while parabolic equations fit in the framework of the parabolic H-measures developed by Antoni\u0107 and Lazar (2007\u20132013). More recently the study of differential relations with fractional derivatives prompted the extension of the theory to arbitrary ratios, thus the fractional H-measures were introduced and applied to fractional conservation laws by Mitrovi\u0107 and Ivec (Commun Pure Appl Anal 10(6):1617\u20131627, 2011). In this paper we explore the transport property of fractional H-measures by studying fractional derivatives of commutators of multiplication and Fourier multiplier operators. In particular, we prove the Second commutation lemma suitable for fractional H-measures, comprehending the known hyperbolic and parabolic cases, while allowing for derivation of the corresponding propagation principle for fractional H-measures. At the end, on a model example we present this derivation of the transport equation for the fractional H-measure.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s11868-017-0207-y", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": false, 
    "isPartOf": [
      {
        "id": "sg:journal.1136558", 
        "issn": [
          "1662-9981", 
          "1662-999X"
        ], 
        "name": "Journal of Pseudo-Differential Operators and Applications", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "3", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "9"
      }
    ], 
    "name": "Second commutation lemma for fractional H-measures", 
    "pagination": "589-613", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "84ece452b05517566452e1b5558400dd6b19e792bdcf42e44f9d06550cc7b281"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s11868-017-0207-y"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1085073693"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s11868-017-0207-y", 
      "https://app.dimensions.ai/details/publication/pub.1085073693"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T10:16", 
    "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/v90/0000000348_0000000348/records_54301_00000001.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://link.springer.com/10.1007%2Fs11868-017-0207-y"
  }
]
 

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/s11868-017-0207-y'

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/s11868-017-0207-y'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s11868-017-0207-y'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s11868-017-0207-y'


 

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

133 TRIPLES      21 PREDICATES      46 URIs      19 LITERALS      7 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s11868-017-0207-y schema:about anzsrc-for:01
2 anzsrc-for:0101
3 schema:author N4fa83eceb23b44dca65835e6775924a8
4 schema:citation sg:pub.10.1007/978-3-540-49938-1
5 sg:pub.10.1007/b138375
6 sg:pub.10.1007/s00009-016-0699-3
7 sg:pub.10.1007/s10958-009-9434-y
8 https://doi.org/10.1016/j.anihpc.2010.10.002
9 https://doi.org/10.1016/j.camwa.2010.09.022
10 https://doi.org/10.1016/j.jfa.2013.06.006
11 https://doi.org/10.1016/j.jfa.2014.12.008
12 https://doi.org/10.1016/j.jfa.2017.01.006
13 https://doi.org/10.1016/j.jmaa.2007.12.077
14 https://doi.org/10.1016/j.nonrwa.2008.07.010
15 https://doi.org/10.1017/s0308210500020606
16 https://doi.org/10.1017/s0308210500023325
17 https://doi.org/10.1080/03605309108820822
18 https://doi.org/10.1080/03605309208820905
19 https://doi.org/10.1155/2011/901084
20 https://doi.org/10.2298/fil1716027e
21 https://doi.org/10.3934/cpaa.2011.10.1617
22 https://doi.org/10.4310/dpde.2012.v9.n3.a3
23 schema:datePublished 2018-09
24 schema:datePublishedReg 2018-09-01
25 schema:description Classical H-measures introduced by Tartar (Proc R Soc Edinb 115A:193–230, 1990) and independently by Gérard (Commun Partial Differ Equ 16:1761–1794, 1991) are essentially suited for hyperbolic equations while parabolic equations fit in the framework of the parabolic H-measures developed by Antonić and Lazar (2007–2013). More recently the study of differential relations with fractional derivatives prompted the extension of the theory to arbitrary ratios, thus the fractional H-measures were introduced and applied to fractional conservation laws by Mitrović and Ivec (Commun Pure Appl Anal 10(6):1617–1627, 2011). In this paper we explore the transport property of fractional H-measures by studying fractional derivatives of commutators of multiplication and Fourier multiplier operators. In particular, we prove the Second commutation lemma suitable for fractional H-measures, comprehending the known hyperbolic and parabolic cases, while allowing for derivation of the corresponding propagation principle for fractional H-measures. At the end, on a model example we present this derivation of the transport equation for the fractional H-measure.
26 schema:genre research_article
27 schema:inLanguage en
28 schema:isAccessibleForFree false
29 schema:isPartOf N597afb34470a4325afe985e3e4b22124
30 Nae4cc6057af84c20b801192abf4d25fa
31 sg:journal.1136558
32 schema:name Second commutation lemma for fractional H-measures
33 schema:pagination 589-613
34 schema:productId N7be154b53c764416bff8df35246505a7
35 N90d4f4a438bc4dfc8ba0f4b4f2ad7858
36 Ncf7c2d3aa8ed44d2ac3b8ee1b4254a9f
37 schema:sameAs https://app.dimensions.ai/details/publication/pub.1085073693
38 https://doi.org/10.1007/s11868-017-0207-y
39 schema:sdDatePublished 2019-04-11T10:16
40 schema:sdLicense https://scigraph.springernature.com/explorer/license/
41 schema:sdPublisher Ne002c100e9aa43e680b91bc776ab776a
42 schema:url https://link.springer.com/10.1007%2Fs11868-017-0207-y
43 sgo:license sg:explorer/license/
44 sgo:sdDataset articles
45 rdf:type schema:ScholarlyArticle
46 N4a081efcb8a54fc38bb25a7890f04844 rdf:first sg:person.012334333661.49
47 rdf:rest rdf:nil
48 N4fa83eceb23b44dca65835e6775924a8 rdf:first sg:person.014772635175.37
49 rdf:rest N4a081efcb8a54fc38bb25a7890f04844
50 N597afb34470a4325afe985e3e4b22124 schema:issueNumber 3
51 rdf:type schema:PublicationIssue
52 N7be154b53c764416bff8df35246505a7 schema:name dimensions_id
53 schema:value pub.1085073693
54 rdf:type schema:PropertyValue
55 N90d4f4a438bc4dfc8ba0f4b4f2ad7858 schema:name readcube_id
56 schema:value 84ece452b05517566452e1b5558400dd6b19e792bdcf42e44f9d06550cc7b281
57 rdf:type schema:PropertyValue
58 Nae4cc6057af84c20b801192abf4d25fa schema:volumeNumber 9
59 rdf:type schema:PublicationVolume
60 Ncf7c2d3aa8ed44d2ac3b8ee1b4254a9f schema:name doi
61 schema:value 10.1007/s11868-017-0207-y
62 rdf:type schema:PropertyValue
63 Ne002c100e9aa43e680b91bc776ab776a schema:name Springer Nature - SN SciGraph project
64 rdf:type schema:Organization
65 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
66 schema:name Mathematical Sciences
67 rdf:type schema:DefinedTerm
68 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
69 schema:name Pure Mathematics
70 rdf:type schema:DefinedTerm
71 sg:journal.1136558 schema:issn 1662-9981
72 1662-999X
73 schema:name Journal of Pseudo-Differential Operators and Applications
74 rdf:type schema:Periodical
75 sg:person.012334333661.49 schema:affiliation https://www.grid.ac/institutes/grid.4808.4
76 schema:familyName Ivec
77 schema:givenName Ivan
78 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.012334333661.49
79 rdf:type schema:Person
80 sg:person.014772635175.37 schema:affiliation https://www.grid.ac/institutes/grid.5970.b
81 schema:familyName Erceg
82 schema:givenName Marko
83 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.014772635175.37
84 rdf:type schema:Person
85 sg:pub.10.1007/978-3-540-49938-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025664356
86 https://doi.org/10.1007/978-3-540-49938-1
87 rdf:type schema:CreativeWork
88 sg:pub.10.1007/b138375 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008312238
89 https://doi.org/10.1007/b138375
90 rdf:type schema:CreativeWork
91 sg:pub.10.1007/s00009-016-0699-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049531261
92 https://doi.org/10.1007/s00009-016-0699-3
93 rdf:type schema:CreativeWork
94 sg:pub.10.1007/s10958-009-9434-y schema:sameAs https://app.dimensions.ai/details/publication/pub.1005787696
95 https://doi.org/10.1007/s10958-009-9434-y
96 rdf:type schema:CreativeWork
97 https://doi.org/10.1016/j.anihpc.2010.10.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035902472
98 rdf:type schema:CreativeWork
99 https://doi.org/10.1016/j.camwa.2010.09.022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1028042753
100 rdf:type schema:CreativeWork
101 https://doi.org/10.1016/j.jfa.2013.06.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1003062744
102 rdf:type schema:CreativeWork
103 https://doi.org/10.1016/j.jfa.2014.12.008 schema:sameAs https://app.dimensions.ai/details/publication/pub.1002109903
104 rdf:type schema:CreativeWork
105 https://doi.org/10.1016/j.jfa.2017.01.006 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010943305
106 rdf:type schema:CreativeWork
107 https://doi.org/10.1016/j.jmaa.2007.12.077 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025629115
108 rdf:type schema:CreativeWork
109 https://doi.org/10.1016/j.nonrwa.2008.07.010 schema:sameAs https://app.dimensions.ai/details/publication/pub.1043410349
110 rdf:type schema:CreativeWork
111 https://doi.org/10.1017/s0308210500020606 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054893743
112 rdf:type schema:CreativeWork
113 https://doi.org/10.1017/s0308210500023325 schema:sameAs https://app.dimensions.ai/details/publication/pub.1054894015
114 rdf:type schema:CreativeWork
115 https://doi.org/10.1080/03605309108820822 schema:sameAs https://app.dimensions.ai/details/publication/pub.1022528357
116 rdf:type schema:CreativeWork
117 https://doi.org/10.1080/03605309208820905 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005526371
118 rdf:type schema:CreativeWork
119 https://doi.org/10.1155/2011/901084 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035722565
120 rdf:type schema:CreativeWork
121 https://doi.org/10.2298/fil1716027e schema:sameAs https://app.dimensions.ai/details/publication/pub.1101870230
122 rdf:type schema:CreativeWork
123 https://doi.org/10.3934/cpaa.2011.10.1617 schema:sameAs https://app.dimensions.ai/details/publication/pub.1071731755
124 rdf:type schema:CreativeWork
125 https://doi.org/10.4310/dpde.2012.v9.n3.a3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1072459723
126 rdf:type schema:CreativeWork
127 https://www.grid.ac/institutes/grid.4808.4 schema:alternateName University of Zagreb
128 schema:name Faculty of Metallurgy, University of Zagreb, Aleja narodnih heroja 3, Sisak, Croatia
129 rdf:type schema:Organization
130 https://www.grid.ac/institutes/grid.5970.b schema:alternateName International School for Advanced Studies
131 schema:name Department of Mathematics, Faculty of Science, University of Zagreb, Bijenička cesta 30, Zagreb, Croatia
132 Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, Trieste, Italy
133 rdf:type schema:Organization
 




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


...