On the Regularity of a Boundary Point for the p(x)-Laplacian

Yu. A. Alkhutova,* and M. D. Surnachevb
Translated by I. Ruzanova

a Vladimir State University, Vladimir, 600000 Russia

b Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia

Correspondence to: *e-mail: yurij-alkhutov@yandex.ru

Received 11 October, 2017

Abstract—The Dirichlet problem for the p(x)-Laplacian with a continuous boundary function is considered, and a sufficient condition is found for the continuity of its solution at a boundary point, assuming that the exponent p(x) satisfies the log-Hölder continuity condition at this point.

DOI: 10.1134/S1064562418010210