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

2021/09/10 by M. van den Berg, Berg, Michiel van den, Andrea Malchiodi +1
Computer Science · Mathematics · #Analysis of PDEs (math.AP) #Analytic and geometric function theory #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · doi:10.48550/arxiv.2109.04915

openalex publication_date 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the existence of a maximiser among open, bounded, convex sets in \R^d, d≥ 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.

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