Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger's equation
Analysis of PDEs
2025-06-24 v2
Abstract
We show that stricty positive viscosity supersolutions to Trudinger's equation are local weak supersolutions when . As an application, we show using the Ishii-Lions method that not only viscosity but also weak solutions are Lipschitz continuous in the space variable. To the best of our knowledge, there is no preceding valid Lipschitz proofs in the literature.
Cite
@article{arxiv.2502.14670,
title = {Lipschitz continuity and equivalence of positive viscosity and weak solutions to Trudinger's equation},
author = {Peter Lindqvist and Mikko Parviainen and Jarkko Siltakoski},
journal= {arXiv preprint arXiv:2502.14670},
year = {2025}
}