Counterexamples to quasiconcavity for the heat equation

Abstract

We construct solutions to the heat equation on convex rings showing that quasiconcavity may not be preserved along the flow, even for smooth and subharmonic initial data.

12 pages, 1 figure. v2 Final version with minor corrections, to appear in Int. Math. Res. Not

References in corpus (2)

• A Microscopic Convexity Principle for Nonlinear Partial Differential Equations
• Curvature estimates for the level set of spatial quasiconcave solutions to a class of parabolic equations

Cited by in corpus (3)

• To logconcavity and beyond
• The Stefan problem and concavity
• Weak Harnack inequalities for eigenvalues and constant rank theorems