We consider the Dirichlet problem for the p-Laplacian with weight and continuous boundary function in a domain D divided into two parts by the hyperplane Σ. The weight is equal to 1 in some part of the domain D and coincides with a small parameter ε in the other. We estimate the modulus of continuity for the solution at a boundary point x0 ∈ ∂D ∩ Σ with a constant independent of ε.
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Dedicated to the 80th anniversary of Vasilii Vasil’evich Zhikov
Translated from Problemy Matematicheskogo Analiza 105, 2020, pp. 3-17.
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Alkhutov, Y.A., Surnachev, M.D. The Boundary Behavior of a Solution to the Dirichlet Problem for the p-Laplacian with Weight Uniformly Degenerate on a Part of Domain with Respect to Small Parameter. J Math Sci 250, 183–200 (2020). https://doi.org/10.1007/s10958-020-05010-w
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DOI: https://doi.org/10.1007/s10958-020-05010-w