On some variational problems involving capacity, torsional rigidity, perimeter and measure

Michiel van den Berg; Andrea Malchiodi

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arXiv · 2109.04915

On some variational problems involving capacity, torsional rigidity, perimeter and measure

Michiel van den Berg·Andrea Malchiodi

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Abstract

We investigate the existence of a maximiser among open, bounded, convex sets in $\R^d,\,d\ge 3$ for the product of torsional rigidity and Newtonian capacity (or logarithmic capacity if $d=2$), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.

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Michiel van den Berg, Andrea Malchiodi. 2021-09-10. On some variational problems involving capacity, torsional rigidity, perimeter and measure. https://arxiv.org/abs/2109.04915

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