%0 Journal Article
%T Integral and isocapacitary inequalities
%A Vladimir Maz'ya
%J Mathematics
%D 2008
%I arXiv
%X 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 $L_p$-norm of the gradient are found.
%U http://arxiv.org/abs/0809.2511v1