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

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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… Click to show full 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.

Keywords: point laplacian; regularity boundary; point; boundary point

Journal Title: Doklady Mathematics
Year Published: 2018

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