Hölder continuity of solutions of an elliptic equation uniformly degenerating on part of the domain
Yu. A. Alkhutov, S. T. Guseinov · Differential Equations · 2009
We consider a second-order divergence elliptic equation in a domain D divided by a hyperplane in two parts. The equation is uniformly elliptic in one of these parts and is uniformly degenerate with respect to a small parameter ɛ in the other. We show that each solution is Hölder continuous in D with Hölder exponent independent of ɛ .