Title

Symmetrization of Poisson's equation with Neumann Boundary Conditions

Publication Date

2015

Journal

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Volume

14

Issue

4

First Page

1025

Last Page

1063

Abstract

In this paper, we compare the solutions of two PDEs with Neumann boundary conditions, one with given initial data and one with cap symmetrized data. We show that the solution with cap symmetrized data is itself cap symmetrized and exhibits larger convex means. As corollaries, we prove comparison results on spheres and hemispheres, and prove a conjecture of B. Kawohl.

DOI

10.2422/2036-2145.201209_003

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