Two isoperimetric inequalities for the Sobolev constant
Analysis of PDEs
2016-02-02 v1
Abstract
In this note we prove two isoperimetric inequalities for the sharp constant in the Sobolev embedding and its associated extremal function. The first such inequality is a variation on the classical Schwarz Lemma from complex analysis, similar to recent inequalities of Burckel, Marshall, Minda, Poggi-Corradini, and Ransford, while the second generalises an isoperimetric inequality for the first eigenfunction of the Laplacian due to Payne and Rayner.
Cite
@article{arxiv.1105.2719,
title = {Two isoperimetric inequalities for the Sobolev constant},
author = {Tom Carroll and Jesse Ratzkin},
journal= {arXiv preprint arXiv:1105.2719},
year = {2016}
}
Comments
11 pages