Hölder continuity of solutions to parabolic equations uniformly degenerating on a part of the domain. (English) Zbl 1254.35107

Summary: 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 \({\varepsilon}\).


35K10 Second-order parabolic equations
35B65 Smoothness and regularity of solutions to PDEs
35D30 Weak solutions to PDEs
Full Text: Euclid