Convex hull property for elliptic and parabolic systems of PDE
Analysis of PDEs
2023-11-29 v1
Abstract
We study the convex hull property for systems of partial differential equations. This is a generalisation of the maximum principle for a single equation. We show that the convex hull property holds for a class of elliptic and parabolic systems of non-linear partial differential equations. In particular, this includes the case of the parabolic -Laplace system. The coupling conditions for coefficients are demonstrated to be optimal by means of respective counterexamples.
Keywords
Cite
@article{arxiv.2311.16949,
title = {Convex hull property for elliptic and parabolic systems of PDE},
author = {Antonín Češík},
journal= {arXiv preprint arXiv:2311.16949},
year = {2023}
}
Comments
16 pages