Hölder continuity of solutions to parabolic equations uniformly degenerating on a part of the domain

Abstract

We study a second-order parabolic equation in divergence form in a spatial domain separated in two parts by a hyperplane. The equation is uniformly parabolic in one of the parts and degenerates with respect to a small parameter $\varepsilon$ on the other part. We show that weak solutions to this equation are Hölder continuous with the Hölder exponent independent of ${\varepsilon}$.