Behavior of solutions of the Dirichlet problem for the \(p(x)\)-Laplacian at a boundary point. (English. Russian original) Zbl 1437.35401
St. Petersbg. Math. J. 31, No. 2, 251-271 (2020); translation from Algebra Anal. 31, No. 2, 88-117 (2019).
Summary: 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.
MSC:
| 35J92 | Quasilinear elliptic equations with \(p\)-Laplacian |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35B65 | Smoothness and regularity of solutions to PDEs |
References:
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