Parabolic quasi-concavity for solutions to parabolic problems in convex rings

Abstract

We investigate some geometric properties of level sets of the solutions of parabolic problems in convex rings. We introduce the notion of parabolic quasi-concavity, which involves time and space jointly and is a stronger property than the spatial quasi-concavity, and study the convexity of superlevel sets of the solutions. © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.