Capacitary measures in fractional order Sobolev spaces: Compactness and applications to minimization problems

Autor:	Lentz, Anna
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Mathematics - Optimization and Control 49K30 28A33 31A15
Druh dokumentu:	Working Paper
Popis:	Capacitary measures form a class of measures that vanish on sets of capacity zero. These measures are compact with respect to so-called $\gamma$-convergence, which relates a sequence of measures to the sequence of solutions of relaxed Dirichlet problems. This compactness result is already known for the classical $H^1(\Omega)$-capacity. This paper extends it to the fractional capacity defined for fractional order Sobolev spaces $H^s(\Omega)$ for $s\in (0,1)$. The compactness result is applied to obtain a finer optimality condition for a class of minimization problems in $H^s(\Omega)$. Comment: 31 pages, 11 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.11876 Zobrazit plný text záznamu View this record from Arxiv