Peer-Reviewed Journal Details
Mandatory Fields
Tom Carroll and Jesse Ratzkin
2012
October
Zeitschrift Fur Angewandte Mathematik Und Physik
Two isoperimetric inequalities for the Sobolev constant
Published
WOS: 4 ()
Optional Fields
63
5
855
863
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 generalizes an 
isoperimetric inequality for the first eigenfunction of the Laplacian 
due to Payne and Rayner. 
0044-2275
10.1007/s00033-012-0198-8
Grant Details