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