Local Hölder continuity for doubly nonlinear parabolic equations

Abstract

We give a proof of the Hölder continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling non-trivial Borel measure which supports a Poincaré inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.

Cited by in corpus (2)

• The Fisher-KPP problem with doubly nonlinear diffusion
• Hölder regularity for parabolic De Giorgi classes in metric measure spaces