Local Hölder continuity for doubly nonlinear parabolic equations

Details Local Hölder continuity for doubly nonlinear parabolic equations Local Hölder continuity for doubly nonlinear parabolic equations

2010-06-04

arxiv.org/abs/1006.0781v2

Indiana Univ. Math. J., 2011

Mathematics

Analysis of PDEs

Scientific paper

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.

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