Calculus of Variations and Geometric Measure Theory

M. van den Berg - A. Malchiodi

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

created by malchiodi on 14 Sep 2021
modified on 24 Jan 2022



Inserted: 14 sep 2021
Last Updated: 24 jan 2022

Pages: 18
Year: 2021

ArXiv: 2109.04915 PDF


We investigate the existence of a maximiser among open, bounded, convex sets in $\mathbb{R}^d,\,d\geq 3$ 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.