Local Hölder continuity for doubly nonlinear parabolic equations

Tuomo Kuusi, Juhana Siljander, José Miguel Urbano

Published 2010-06-04, updated 2010-09-24Version 2

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 non-trivial Borel measure which supports a Poincar\'e inequality. The proof discriminates between large scales, for which a Harnack inequality is used, and small scales, that require intrinsic scaling methods.