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Sibirskii Matematicheskii Zhurnal, 2018, Volume 59, Number 6, Pages 1291–1302
DOI: https://doi.org/10.17377/smzh.2018.59.606 (Mi smj3044) 		 
This article is cited in 4 scientific papers (total in 4 papers)

The Poincaré inequality and $p$-connectedness of a stratified set

N. S. Dairbekov, O. M. Penkin, L. O. Sarybekova

Kazakh-British Technical University, Almaty, Kazakhstan
Full-text PDF (348 kB) Citations (4)
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DOI: https://doi.org/10.17377/smzh.2018.59.606
Abstract: We extend the Poincaré inequality to functions of Sobolev type on a stratified set. The integrability exponents in these analogs depend on the geometric characteristics of the stratified set which show to what extent their strata are connected with each other and the boundary. We apply the results to proving the solvability of boundary value problems for the $p$-Laplacian with boundary conditions of Neumann or Wentzel type.
Keywords: Poincaré inequality, stratified set, $p$-Laplacian.
Funding agency Grant number
Ministry of Education and Science of the Republic of Kazakhstan АР05130222
The authors were supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grant AR05130222).
Received: 11.04.2018
English version:
Siberian Mathematical Journal, 2018, Volume 59, Issue 6, Pages 1024–1033
DOI: https://doi.org/10.1134/S003744661806006X
Bibliographic databases:
Document Type: Article
UDC: 517.51+517.95
Language: Russian
Citation: N. S. Dairbekov, O. M. Penkin, L. O. Sarybekova, “The Poincaré inequality and $p$-connectedness of a stratified set”, Sibirsk. Mat. Zh., 59:6 (2018), 1291–1302; Siberian Math. J., 59:6 (2018), 1024–1033
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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