Yu. A. Alkhutov, M. D. Surnachev, “Interior and boundary continuity of <nobr>$p(x)$</nobr>-harmonic functions”, Zap. Nauchn. Sem. POMI, 2021, Volume 508,Pages <nobr>7

Interior and boundary continuity of $p(x)$-harmonic functions

Yu. A. Alkhutov^a, M. D. Surnachev^b

^a Vladimir State University
^b Keldysh Institute of Applied Mathematics of Russian Academy of Sciences, Moscow

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.

UDC: 517

Received: 26.10.2021