IUMJ

Title: Local Hoelder continuity for doubly nonlinear parabolic equations

Authors: Tuomo Kuusi, Juhana Siljander and Jose Miguel Urbano

Issue: Volume 61 (2012), Issue 1, 399-430

Abstract:

We give a proof of the H\"older continuity of weak solutions of certain degenerate doubly nonlinear parabolic equations in measure spaces. We only assume the measure to be a doubling nontrivial Borel measure which supports a Poincar\'e inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, which require intrinsic scaling methods.