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

Yu. A. Alkhutov ; M. D. Surnachev

Algebra i analiz, Tome 31 (2019) no. 2, pp. 88-117.

Résumé

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.

Détail

Keywords: Wiener criterion, boundary regularity, Dirichlet problem, variable exponent, $p(x)$-Laplacian.

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