The Stefan problem and concavity

Abstract

We construct examples for the one-phase Stefan problem which show that $\alpha$-concavity of the solution is in general not preserved in time, for $0\le \alpha <1/2$. In particular, this shows that, in contrast to the case of the heat equation for a fixed convex domain, log concavity is not preserved for solutions of the Stefan problem.

12 pages

References in corpus (1)

• Counterexamples to quasiconcavity for the heat equation

Cited by in corpus (1)

• On Concavity of Solutions of the Nonlinear Poisson Equation