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.
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Original Russian Text © Yu.A. Alkhutov, M.D. Surnachev, 2018, published in Doklady Akademii Nauk, 2018, Vol. 478, No. 5, pp. 505–508.
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Alkhutov, Y.A., Surnachev, M.D. On the Regularity of a Boundary Point for the p(x)-Laplacian. Dokl. Math. 97, 65–68 (2018). https://doi.org/10.1134/S1064562418010210
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DOI: https://doi.org/10.1134/S1064562418010210