Neumann Comparison Theorems in Elliptic PDEs
Publication Date
2015
Description
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.
Journal
Potential Analysis
Volume
43
Issue
3
First Page
415
Last Page
459
Department
Mathematics
Link to Published Version
DOI
10.1007/s11118-015-9479-0
Recommended Citation
Langford, Jeffrey J.. "Neumann Comparison Theorems in Elliptic PDEs." Potential Analysis (2015) : 415-459.
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