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.
Parabolic quasi-concavity for solutions to parabolic problems in convex rings / K. Ishiige; P. Salani. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - STAMPA. - 283 issue 11:(2010), pp. 1526-1548. [10.1002/mana.200910242]
Parabolic quasi-concavity for solutions to parabolic problems in convex rings
SALANI, PAOLO
2010
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.
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