Boyarsky–Meyers Estimate for Solutions to Zaremba Problem View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

2022-06-29

AUTHORS

Yurij A. Alkhutov, Gregory A. Chechkin, Vladimir G. Maz’ya

ABSTRACT

The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2+\delta }$$\end{document}, δ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta >0$$\end{document}, for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n-1)$$\end{document}-dimensional measure and non-zero p-capacity, p>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>1$$\end{document} is constructed. More... »

PAGES

1197-1211

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00205-022-01805-0

DOI

http://dx.doi.org/10.1007/s00205-022-01805-0

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1149066683


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/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "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/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "A.G. and N.G. Stoletov Vladimir State University, Stroitelej st., 11, Vladimir, Russia", 
          "id": "http://www.grid.ac/institutes/grid.171855.f", 
          "name": [
            "A.G. and N.G. Stoletov Vladimir State University, Stroitelej st., 11, Vladimir, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Alkhutov", 
        "givenName": "Yurij A.", 
        "id": "sg:person.016140512235.22", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016140512235.22"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan", 
          "id": "http://www.grid.ac/institutes/grid.473156.2", 
          "name": [
            "M.V. Lomonosov Moscow State University, Leninskie gory, 1, Moscow, Russia", 
            "Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, Russia", 
            "Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Chechkin", 
        "givenName": "Gregory A.", 
        "id": "sg:person.013311053516.59", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013311053516.59"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "RUDN University, Miklukho-Maklaya St, 6, Moscow, Russia", 
          "id": "http://www.grid.ac/institutes/grid.77642.30", 
          "name": [
            "Link\u00f6pings Universitet, Link\u00f6ping, Sverige", 
            "RUDN University, Miklukho-Maklaya St, 6, Moscow, Russia"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Maz\u2019ya", 
        "givenName": "Vladimir G.", 
        "id": "sg:person.013163454255.54", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013163454255.54"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf02392268", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021666193", 
          "https://doi.org/10.1007/bf02392268"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-662-03282-4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005597834", 
          "https://doi.org/10.1007/978-3-662-03282-4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1134/s1064562421020022", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1139668854", 
          "https://doi.org/10.1134/s1064562421020022"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2022-06-29", 
    "datePublishedReg": "2022-06-29", 
    "description": "The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+\u03b4\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$L_{2+\\delta }$$\\end{document}, \u03b4>0\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$\\delta >0$$\\end{document}, for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n-1)\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$(n-1)$$\\end{document}-dimensional measure and non-zero p-capacity, p>1\\documentclass[12pt]{minimal}\n\t\t\t\t\\usepackage{amsmath}\n\t\t\t\t\\usepackage{wasysym}\n\t\t\t\t\\usepackage{amsfonts}\n\t\t\t\t\\usepackage{amssymb}\n\t\t\t\t\\usepackage{amsbsy}\n\t\t\t\t\\usepackage{mathrsfs}\n\t\t\t\t\\usepackage{upgreek}\n\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\n\t\t\t\t\\begin{document}$$p>1$$\\end{document} is constructed.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/s00205-022-01805-0", 
    "isAccessibleForFree": false, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.9048407", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1047617", 
        "issn": [
          "0003-9527", 
          "1432-0673"
        ], 
        "name": "Archive for Rational Mechanics and Analysis", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "2", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "245"
      }
    ], 
    "keywords": [
      "linear second-order elliptic equation", 
      "second order elliptic equations", 
      "elliptic equations", 
      "variational solution", 
      "measurable coefficients", 
      "Dirichlet data", 
      "fractal sets", 
      "graph domain", 
      "Zaremba problem", 
      "problem", 
      "solution", 
      "p-capacity", 
      "equations", 
      "estimates", 
      "set", 
      "coefficient", 
      "gradient", 
      "dimensional measures", 
      "domain", 
      "data", 
      "measures", 
      "example"
    ], 
    "name": "Boyarsky\u2013Meyers Estimate for Solutions to Zaremba Problem", 
    "pagination": "1197-1211", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1149066683"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00205-022-01805-0"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00205-022-01805-0", 
      "https://app.dimensions.ai/details/publication/pub.1149066683"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-11-24T21:08", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221124/entities/gbq_results/article/article_929.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/s00205-022-01805-0"
  }
]
 

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/s00205-022-01805-0'

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/s00205-022-01805-0'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01805-0'

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

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00205-022-01805-0'


 

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

120 TRIPLES      21 PREDICATES      50 URIs      38 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00205-022-01805-0 schema:about anzsrc-for:01
2 anzsrc-for:0101
3 anzsrc-for:0102
4 schema:author Ne2c2b90c9f584c2ba0d8d78cd04af141
5 schema:citation sg:pub.10.1007/978-3-662-03282-4
6 sg:pub.10.1007/bf02392268
7 sg:pub.10.1134/s1064562421020022
8 schema:datePublished 2022-06-29
9 schema:datePublishedReg 2022-06-29
10 schema:description The variational solution to the Zaremba problem for a divergent linear second order elliptic equation with measurable coefficients is considered. The problem is set in a local Lipschitz graph domain. An estimate in L2+δ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_{2+\delta }$$\end{document}, δ>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\delta >0$$\end{document}, for the gradient of a solution, is proved. An example of the problem with the Dirichlet data supported by a fractal set of zero (n-1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(n-1)$$\end{document}-dimensional measure and non-zero p-capacity, p>1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p>1$$\end{document} is constructed.
11 schema:genre article
12 schema:isAccessibleForFree false
13 schema:isPartOf Na4bf56d288894ad989f5a7690202c586
14 Nc3f771f21e354fa6a95e79e4abd46f26
15 sg:journal.1047617
16 schema:keywords Dirichlet data
17 Zaremba problem
18 coefficient
19 data
20 dimensional measures
21 domain
22 elliptic equations
23 equations
24 estimates
25 example
26 fractal sets
27 gradient
28 graph domain
29 linear second-order elliptic equation
30 measurable coefficients
31 measures
32 p-capacity
33 problem
34 second order elliptic equations
35 set
36 solution
37 variational solution
38 schema:name Boyarsky–Meyers Estimate for Solutions to Zaremba Problem
39 schema:pagination 1197-1211
40 schema:productId N39edbed2c09843dd947ac7cd8155529e
41 N70cb404bff024b2ca62abfde3ba60a8d
42 schema:sameAs https://app.dimensions.ai/details/publication/pub.1149066683
43 https://doi.org/10.1007/s00205-022-01805-0
44 schema:sdDatePublished 2022-11-24T21:08
45 schema:sdLicense https://scigraph.springernature.com/explorer/license/
46 schema:sdPublisher N6c7672ffba5244bab9ec6c41eaba59fd
47 schema:url https://doi.org/10.1007/s00205-022-01805-0
48 sgo:license sg:explorer/license/
49 sgo:sdDataset articles
50 rdf:type schema:ScholarlyArticle
51 N39edbed2c09843dd947ac7cd8155529e schema:name dimensions_id
52 schema:value pub.1149066683
53 rdf:type schema:PropertyValue
54 N6c7672ffba5244bab9ec6c41eaba59fd schema:name Springer Nature - SN SciGraph project
55 rdf:type schema:Organization
56 N70cb404bff024b2ca62abfde3ba60a8d schema:name doi
57 schema:value 10.1007/s00205-022-01805-0
58 rdf:type schema:PropertyValue
59 N7f6bef304efa44bf9bdaf9230d6e4aea rdf:first sg:person.013311053516.59
60 rdf:rest Nfa5c0624cc2f4fd59d03c43a46d3c906
61 Na4bf56d288894ad989f5a7690202c586 schema:issueNumber 2
62 rdf:type schema:PublicationIssue
63 Nc3f771f21e354fa6a95e79e4abd46f26 schema:volumeNumber 245
64 rdf:type schema:PublicationVolume
65 Ne2c2b90c9f584c2ba0d8d78cd04af141 rdf:first sg:person.016140512235.22
66 rdf:rest N7f6bef304efa44bf9bdaf9230d6e4aea
67 Nfa5c0624cc2f4fd59d03c43a46d3c906 rdf:first sg:person.013163454255.54
68 rdf:rest rdf:nil
69 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
70 schema:name Mathematical Sciences
71 rdf:type schema:DefinedTerm
72 anzsrc-for:0101 schema:inDefinedTermSet anzsrc-for:
73 schema:name Pure Mathematics
74 rdf:type schema:DefinedTerm
75 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
76 schema:name Applied Mathematics
77 rdf:type schema:DefinedTerm
78 sg:grant.9048407 http://pending.schema.org/fundedItem sg:pub.10.1007/s00205-022-01805-0
79 rdf:type schema:MonetaryGrant
80 sg:journal.1047617 schema:issn 0003-9527
81 1432-0673
82 schema:name Archive for Rational Mechanics and Analysis
83 schema:publisher Springer Nature
84 rdf:type schema:Periodical
85 sg:person.013163454255.54 schema:affiliation grid-institutes:grid.77642.30
86 schema:familyName Maz’ya
87 schema:givenName Vladimir G.
88 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013163454255.54
89 rdf:type schema:Person
90 sg:person.013311053516.59 schema:affiliation grid-institutes:grid.473156.2
91 schema:familyName Chechkin
92 schema:givenName Gregory A.
93 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.013311053516.59
94 rdf:type schema:Person
95 sg:person.016140512235.22 schema:affiliation grid-institutes:grid.171855.f
96 schema:familyName Alkhutov
97 schema:givenName Yurij A.
98 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.016140512235.22
99 rdf:type schema:Person
100 sg:pub.10.1007/978-3-662-03282-4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005597834
101 https://doi.org/10.1007/978-3-662-03282-4
102 rdf:type schema:CreativeWork
103 sg:pub.10.1007/bf02392268 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021666193
104 https://doi.org/10.1007/bf02392268
105 rdf:type schema:CreativeWork
106 sg:pub.10.1134/s1064562421020022 schema:sameAs https://app.dimensions.ai/details/publication/pub.1139668854
107 https://doi.org/10.1134/s1064562421020022
108 rdf:type schema:CreativeWork
109 grid-institutes:grid.171855.f schema:alternateName A.G. and N.G. Stoletov Vladimir State University, Stroitelej st., 11, Vladimir, Russia
110 schema:name A.G. and N.G. Stoletov Vladimir State University, Stroitelej st., 11, Vladimir, Russia
111 rdf:type schema:Organization
112 grid-institutes:grid.473156.2 schema:alternateName Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
113 schema:name Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan
114 Institute of Mathematics with Computing Center - Subdivision of the Ufa Federal Research Center of Russian Academy of Science, Ufa, Russia
115 M.V. Lomonosov Moscow State University, Leninskie gory, 1, Moscow, Russia
116 rdf:type schema:Organization
117 grid-institutes:grid.77642.30 schema:alternateName RUDN University, Miklukho-Maklaya St, 6, Moscow, Russia
118 schema:name Linköpings Universitet, Linköping, Sverige
119 RUDN University, Miklukho-Maklaya St, 6, Moscow, Russia
120 rdf:type schema:Organization
 




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


...