Local H\"older continuity for some doubly nonlinear parabolic equations   in measure spaces
  We establish the local H\"older 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 Poincar\'e inequality. 
Eurica Henriques and Rojbin Laleoglu
math.AP