Integral and isocapacitary inequalities
Functional Analysis
2008-09-16 v1 Analysis of PDEs
Abstract
It is shown by a counterexample that isocapacitary and isoperimetric constants of a multi-dimensional Euclidean domain starshaped with respect to a ball are not equivalent. Sharp integral inequalities involving the harmonic capacity which imply Faber-Krahn property of the fundamental Dirichlet-Laplace eigenvalue are obtained. Necessary and sufficient conditions ensuring integral inequalities between a difference seminorm and the -norm of the gradient are found.
Cite
@article{arxiv.0809.2511,
title = {Integral and isocapacitary inequalities},
author = {Vladimir Maz'ya},
journal= {arXiv preprint arXiv:0809.2511},
year = {2008}
}