The De Giorgi method for local and nonlocal systems
Analysis of PDEs
2024-04-08 v1
Abstract
We extend the De Giorgi iteration technique to the vectorial setting. For this we replace the usual scalar truncation operator by a vectorial shortening operator. As an application, we prove local boundedness for local and nonlocal nonlinear systems. Furthermore, we show convex hull properties, which are a generalization of the maximum principle to the case of systems.
Cite
@article{arxiv.2404.04063,
title = {The De Giorgi method for local and nonlocal systems},
author = {Linus Behn and Lars Diening and Simon Nowak and Toni Scharle},
journal= {arXiv preprint arXiv:2404.04063},
year = {2024}
}