On the continuity of solutions to elliptic equations with variable order of nonlinearity
Yu. A. Alkhutov, О. В. Крашенинникова · Proceedings of the Steklov Institute of Mathematics · 2008
We study the p -Laplacian with variable exponent p ( x ) bounded away from unity and infinity. We obtain a sufficient condition on p ( x ) under which all solutions of the p -Laplace equation are continuous at a fixed point of a domain, and find an estimate for the modulus of continuity of solutions.