H\"older continuity for Trudinger's equation in measure spaces
  We complete the study of the regularity for Trudinger's equation by proving that weak solutions are H\"older continuous also in the singular case. The setting is that of a measure space with a doubling non-trivial Borel measure supporting a Poincar\'e inequality. The proof uses the Harnack inequality and intrinsic scaling. 
Tuomo Kuusi, Rojbin Laleoglu, Juhana Siljander and Jos\'e Miguel   Urbano
math.AP