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.
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
\Bibitem{DaiPenSar18}
\by N.~S.~Dairbekov, O.~M.~Penkin, L.~O.~Sarybekova
\paper The Poincar\'e inequality and $p$-connectedness of a~stratified set
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 6
\pages 1291--1302
\mathnet{http://mi.mathnet.ru/smj3044}
\crossref{https://doi.org/10.17377/smzh.2018.59.606}
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\transl
\jour Siberian Math. J.
\yr 2018
\vol 59
\issue 6
\pages 1024--1033
\crossref{https://doi.org/10.1134/S003744661806006X}
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Linking options:
https://www.mathnet.ru/eng/smj3044
https://www.mathnet.ru/eng/smj/v59/i6/p1291
This publication is cited in the following 4 articles:
K. M. Medvedev, A. I. Nazarov, “Otsenka normy Geldera dlya resheniya divergentnogo ellipticheskogo uravneniya na stratifitsirovannom mnozhestve”, Algebra i analiz, 36:1 (2024), 170–194
Nurlan S. Dairbekov, Oleg M. Penkin, Denis V. Savasteev, “Removable Singularities of Harmonic Functions on Stratified Sets”, Symmetry, 16:4 (2024), 486
N. S. Dairbekov, O. M. Penkin, D. V. Savasteev, “Neravenstvo Kharnaka dlya garmonicheskikh funktsii na stratifitsirovannom mnozhestve”, Sib. matem. zhurn., 64:5 (2023), 971–981
N S. Dairbekov, O. M. Penkin, D. V. Savasteev, “Harnack's Inequality for Harmonic Functions on Stratified Sets”, Sib Math J, 64:5 (2023), 1137
Citation in format AMSBIB
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