Behavior of solutions of the Dirichlet Problem for the $p(x)$-Laplacian at a boundary point
Yu. A. Alkhutov, Mikhail Dmitriyevich Surnachev · St Petersburg Mathematical Journal · 2020
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.