Integral and isocapacitary inequalities

Details Integral and isocapacitary inequalities Integral and isocapacitary inequalities

2008-09-15

arxiv.org/abs/0809.2511v1

Mathematics

Functional Analysis

Scientific paper

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.

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