Title

Neumann Comparison Theorems in Elliptic PDEs

Publication Date

2015

Journal

Potential Analysis

Volume

43

Issue

3

First Page

415

Last Page

459

Abstract

In this paper we prove a spherical comparison result for the (k,n)-spherical rearrangement using the spherical Green's function and a rearrangement inequality of A. Baernstein. We next use a simple reflection argument to obtain a Neumann comparison result on a hemisphere for the (k,n)-hemispherical rearrangement. Using the Lambert equal-area projection and stereographic projection, we obtain Neumann comparison results in Euclidean space. We end with a discussion of open problems in the unit disk involving heat flow.

DOI

10.1007/s11118-015-9479-0

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