We investigate the existence of a maximiser among open, bounded, convex sets in $R^d,,dge 3$ 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.
On some variational problems involving capacity, torsional rigidity, perimeter and measure
Andrea Malchiodi
2023
Abstract
We investigate the existence of a maximiser among open, bounded, convex sets in $R^d,,dge 3$ 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.File in questo prodotto:
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Open Access dal 23/06/2023
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