M. van den Berg - A. Malchiodi
On some variational problems involving capacity, torsional rigidity, perimeter and measure
Preprint
Inserted: 14 sep 2021
Last Updated: 24 jan 2022
Pages: 18
Year: 2021
Abstract:
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.
Download: