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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)



Behavior of solutions of the Dirichlet Problem for the $ p(x)$-Laplacian at a boundary point

Authors: Yu. A. Alkhutov and M. D. Surnachev
Translated by: E. Peller
Original publication: Algebra i Analiz, tom 31 (2019), nomer 2.
Journal: St. Petersburg Math. J. 31 (2020), 251-271
MSC (2010): Primary 35J57, 35J67, 35J92; Secondary 35J15
Published electronically: February 4, 2020
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Abstract: The Dirichlet problem for the $ p(x)$-Laplacian with a continuous boundary function is treated. A sufficient condition is indicated for the regularity of a boundary point, and the modulus of continuity of solutions at this point is estimated.

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Additional Information

Yu. A. Alkhutov
Affiliation: Vladimir State University named after Alexander and Nikolay Stoletov, Gor′kogo st. 87, 600000 Vladimir, Russia

M. D. Surnachev
Affiliation: Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Miusskaya pl. 4, 125047 Moscow, Russia

Keywords: Wiener criterion, boundary regularity, Dirichlet problem, variable exponent, $p(x)$-Laplacian
Received by editor(s): October 31, 2018
Published electronically: February 4, 2020
Additional Notes: The work was supported by the Ministry of Education and Science of the Russian Federation (grant 1.3270.2017/4.6) and Russian Foundation for Basic Research (grant 19-01-00184-a)
Dedicated: To Vladimir Gilelevich Maz’ya Blessed are those who find wisdom Book of Proverbs, Chapter 3, Proverb 13
Article copyright: © Copyright 2020 American Mathematical Society