Holder Continuity of Solutions of an Elliptic p(x)-Laplace Equation Uniformly Degenerate on a Part of the Domain

摘要

In a domain D subset of Double-struck capital R-n divided by a hyperplane sigma into two parts D-(1) and D-(2), we consider a p(x)-Laplace type equation with a small parameter and with exponent p(x) that has a logarithmic modulus of continuity in each part of the domain and undergoes a jump on sigma when passing from D-(2) to D-(1). Under the assumption that the equation uniformly degenerates with respect to the small parameter in D-(1), we establish the Holder continuity of solutions with Holder exponent independent of the parameter.