Sharp Hölder regularity for the inhomogeneous Trudinger’s equation

Abstract

We show that locally bounded solutions of the inhomogeneous Trudinger’s equation are locally Hölder continuous with exponent where α 0 denotes the optimal Hölder exponent for solutions of the homogeneous case. We provide a streamlined proof, using the full power of the homogeneity in the equation to develop the regularity analysis in the p-parabolic geometry, without any need of intrinsic scaling, as anticipated by Trudinger. The main difficulty in the proof is to overcome the lack of a translation invariance property.