Hölder continuity for Trudinger's equation in measure spaces
The authors consider the so-called Trudinger equations, i.e., quasilinear parabolic equations of the type \[ u^{p-1}_t = \nabla ( |\nabla u |^{p-2}\nabla u). \] They study the singular case (i.e., the case \(1<p<2\)). The authors already proved the Hölder regularity of the solutions for such kind of equations for the degenerate case in the setting of a measure space with a doubling non-trivial Borel measure supporting a Poincaré inequality. In this paper, the authors extend this result to the singular case. In the proof, the authors use some recent Harnack estimates and an intrinsic scaling approach.
scientific article; zbMATH DE number 6087752
scientific article