Calculus of Variations and Geometric Measure Theory

P. Acampora - E. Cristoforoni

An isoperimetric result for an energy related to the $p$-capacity

created by acampora on 05 Jul 2024



Inserted: 5 jul 2024

Year: 2022

ArXiv: 2207.14582 PDF


In this paper, we generalize the notion of relative $p$-capacity of $K$ with respect to $\Omega$, by replacing the Dirichlet boundary condition with a Robin one. We show that, under volume constraints, our notion of $p$-capacity is minimal when $K$ and $\Omega$ are concentric balls. We use the $H$-function and a derearrangement technique.