H\"older continuity for Trudinger's equation in measure spaces

TL;DR

This paper establishes the H"older continuity of weak solutions to Trudinger's equation in measure spaces with doubling measures and Poincaré inequalities, extending regularity results to the singular case.

Contribution

It proves H"older continuity for solutions in the singular case, completing the regularity theory for Trudinger's equation in measure spaces.

Findings

Weak solutions are H"older continuous in measure spaces.

The proof employs Harnack inequality and intrinsic scaling techniques.

Regularity results now include the singular case.

Abstract

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.