English

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