Convex hull property for elliptic and parabolic systems of PDE

Antonín Češík

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arXiv · 2311.16949

Convex hull property for elliptic and parabolic systems of PDE

Antonín Češík

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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.

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Antonín Češík. 2023-11-28. Convex hull property for elliptic and parabolic systems of PDE. https://arxiv.org/abs/2311.16949

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