On some variational problems involving capacity, torsional rigidity, perimeter and measure
M Berg, A Malchiodi - arXiv preprint arXiv:2109.04915, 2021 - arxiv.org
arXiv preprint arXiv:2109.04915, 2021•arxiv.org
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$), with constraints involving Lebesgue measure or a combination of Lebesgue
measure and perimeter.
d\ge 3$ 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.
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 ), with constraints involving Lebesgue measure or a combination of Lebesgue measure and perimeter.
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