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arXiv · 0809.2511

Integral and isocapacitary inequalities

Vladimir Maz'ya
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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 $L_p$-norm of the gradient are found.

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Vladimir Maz'ya. 2008-09-15. Integral and isocapacitary inequalities. https://arxiv.org/abs/0809.2511

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