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St. Petersburg Mathematical Journal

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An analog of the Sobolev inequality on a stratified set


Authors: N. S. Dairbekov, O. M. Penkin and L. O. Sarybekova
Translated by: V. V. Kapustin
Original publication: Algebra i Analiz, tom 30 (2018), nomer 5.
Journal: St. Petersburg Math. J. 30 (2019), 869-875
MSC (2010): Primary 35K35, 35A05
DOI: https://doi.org/10.1090/spmj/1573
Published electronically: July 26, 2019
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Abstract | References | Similar Articles | Additional Information

Abstract: On a set $ \Omega \subset \mathbb{R}^d$ that is formed from a finite collection of manifolds that adjoin each other in a special way (i.e., on a stratified set) an exact analog of the Sobolev inequality is proved, in which the exponents are expressed via the characteristics of the intrinsic geometric structure of $ \Omega $. The result is applied in order to prove the solvability of the Dirichlet problem for the $ p$-Laplacian.


References [Enhancements On Off] (What's this?)

  • [1] F. Pham, Introduction à l’étude topologique des singularités de Landau, Mémorial des Sciences Mathématiques, Fasc. 164, Gauthier-Villars Éditeur, Paris, 1967 (French). MR 0229263
  • [2] Robert A. Adams, Sobolev spaces, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Pure and Applied Mathematics, Vol. 65. MR 0450957
  • [3] S. L. Sobolev, Some applications of functional analysis in mathematical physics, Translations of Mathematical Monographs, vol. 90, American Mathematical Society, Providence, RI, 1991. Translated from the third Russian edition by Harold H. McFaden; With comments by V. P. Palamodov. MR 1125990
  • [4] A. I. Nazarov and S. V. Poborchiĭ, The Poincaré inequality and its applications, St. Petersburg Univ. Press, St. Petersburg, 2012. (Russian)
  • [5] Yu. V. Pokornyĭ, O. M. Penkin, V. L. Pryadiev, A. V. Borovskikh, K. P. Lazarev, and S. A. Shabrov, Differentsial′nye uravneniya na geometricheskikh grafakh, Fiziko-Matematicheskaya Literatura, Moscow, 2005 (Russian, with Russian summary). MR 2271942

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Additional Information

N. S. Dairbekov
Affiliation: Kazakh-British Technical university, Tolebi 59, 050000 Almaty, Kazakhstan
Email: nurlan.dairbekov@gmail.com

O. M. Penkin
Affiliation: Kazakh-British Technical university, Tolebi 59, 050000 Almaty, Kazakhstan
Email: o.m.penkin@gmail.com

L. O. Sarybekova
Affiliation: Kazakh-British Technical university, Tolebi 59, 050000 Almaty, Kazakhstan
Email: lsarybekova@yandex.kz

DOI: https://doi.org/10.1090/spmj/1573
Keywords: Stratified set, Sobolev inequality
Received by editor(s): June 14, 2017
Published electronically: July 26, 2019
Additional Notes: The work is partially supported by the grant of the Ministry of Education and Science of Republic of Kazakhstan AP05130222
Article copyright: © Copyright 2019 American Mathematical Society