Title

Subharmonicity, Comparison Results, and Temperature Gaps in Cylindrical Domains

Publication Date

2016

Journal

Differential and Integral Equations

Volume

29

Issue

5-6

First Page

493

Last Page

512

Abstract

In this paper, we compare the solutions of two Poisson PDE’s in cylinders with Neumann boundary conditions, one with given initial data and one with data arranged decreasing in the y−direction. When the solutions are normalized to have zero mean, we show that the solution with symmetrized data is itself symmetrized and exhibits larger convex means. The main tools used are the star function introduced by Baernstein and a new subharmonicity result. As a consequence, we give a new proof of a conjecture of Kawohl for temperature gaps in rectangles.

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