Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point
Yu. A. Alkhutov, M. D. Surnachëv
Abstract
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.
Topics & Concepts
MathematicsDirichlet boundary conditionBoundary (topology)Mathematical analysisDirichlet problemModulus of continuityPoint (geometry)Laplace operatorModulusDirichlet distributionBoundary value problemFunction (biology)GeometryType (biology)BiologyEvolutionary biologyEcologyAdvanced Mathematical Modeling in EngineeringNonlinear Partial Differential EquationsDifferential Equations and Boundary Problems