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Zapiski Nauchnykh Seminarov POMI, 2021, Volume 508, Pages 7–38 (Mi znsl7168)  
Interior and boundary continuity of $p(x)$-harmonic functions

Yu. A. Alkhutova, M. D. Surnachevb

a Vladimir State University
b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow
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Abstract: In this paper we establish results on interior and boundary continuity of $p(x)$-harmonic functions with discontinuous exponent $p(x)$.
Key words and phrases: $p(x)$-Laplacian, logarithminc condition, continuity of solutions, Dirichlet problem, boundary point regularity.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00184
Received: 26.10.2021
English version:
Journal of Mathematical Sciences (New York), 2024, Volume 283, Issue 5, Pages 699–720
DOI: https://doi.org/10.1007/s10958-024-07303-w
Document Type: Article
UDC: 517
Language: Russian
Citation: Yu. A. Alkhutov, M. D. Surnachev, “Interior and boundary continuity of $p(x)$-harmonic functions”, Boundary-value problems of mathematical physics and related problems of function theory. Part 49, Zap. Nauchn. Sem. POMI, 508, POMI, St. Petersburg, 2021, 7–38; J. Math. Sci. (N. Y.), 283:5 (2024), 699–720
Citation in format AMSBIB
\Bibitem{AlkSur21}
\by Yu.~A.~Alkhutov, M.~D.~Surnachev
\paper Interior and boundary continuity of $p(x)$-harmonic functions
\inbook Boundary-value problems of mathematical physics and related problems of function theory. Part~49
\serial Zap. Nauchn. Sem. POMI
\yr 2021
\vol 508
\pages 7--38
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl7168}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2024
\vol 283
\issue 5
\pages 699--720
\crossref{https://doi.org/10.1007/s10958-024-07303-w}
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