On the Continuity of Solutions to Elliptic Equations with Variable Order of Nonlinearity

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.