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.
2023
Settore MAT/05 - Analisi Matematica
Mathematics - Analysis of PDEs; Mathematics - Analysis of PDEs
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/108914
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