Hölder Continuity of Solutions of an Elliptic p(x)-Laplace Equation Uniformly Degenerate on a Part of the Domain
Yu. A. Alkhutov, Sarvan T. Huseynov · Differential Equations · 2019
In a domain D ⊂ ℝ n divided by a hyperplane Σ 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 Σ 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 Hölder continuity of solutions with Hölder exponent independent of the parameter.