Convex hull property for elliptic and parabolic systems of PDE

2023/11/28 by Češík, Antonín · 1 citation
#35B50 #35J47 #35K40 #35K59 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.16949

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 p-Laplace system. The coupling conditions for coefficients are demonstrated to be optimal by means of respective counterexamples.

Cited by

• Existence of global weak solutions to a parabolic p-Laplacian problem with convective term

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