Local Hölder continuity for some doubly nonlinear parabolic equations in measure spaces

Abstract

We establish the local Hölder continuity for the nonnegative weak solutions of certain doubly nonlinear parabolic equations possessing a singularity in the time derivative part and a degeneracy in the principal part. The proof involves the method of intrinsic scaling and the setting is a measure space equipped with a doubling non-trivial Borel measure supporting a Poincaré inequality.

arXiv admin note: text overlap with arXiv:1006.0781 by other authors