Strong space-time convexity and the heat equation
Analysis of PDEs
2021-11-17 v3
Abstract
We prove local strong convexity of the space-time level sets of the heat equation on convex rings for zero initial data, strengthening a result of Borell. Our proof introduces a parabolic version of a two-point maximum principle of Rosay-Rudin.
Keywords
Cite
@article{arxiv.1903.03208,
title = {Strong space-time convexity and the heat equation},
author = {Albert Chau and Ben Weinkove},
journal= {arXiv preprint arXiv:1903.03208},
year = {2021}
}
Comments
17 pages, v2 final version, with minor changes to appear in Indiana Univ. Math. J.; v3 a typo fixed