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arXiv · 1305.6271

Symmetry breaking in a constrained Cheeger type isoperimetric inequality

Barbara Brandolini·Francesco Della Pietra·Carlo Nitsch·Cristina Trombetti
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Abstract

We study the optimal constant in a Sobolev inequality for BV functions with zero mean value and vanishing outside a bounded open set. We are interested in finding the best possible embedding constant in terms of the measure of the domain alone. We set up an optimal shape problem and we completely characterize the behavior of optimal domains.

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Barbara Brandolini, Francesco Della Pietra, Carlo Nitsch, Cristina Trombetti. 2013-11-07. Symmetry breaking in a constrained Cheeger type isoperimetric inequality. https://arxiv.org/abs/1305.6271

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