Korevaar-Schoen p-energies and their Γ-limits on Cheeger spaces

2024/01/28 by Patricia Alonso Ruiz, Ruiz, Patricia Alonso, Fabrice Baudoin +1
Mathematics · #Advanced Harmonic Analysis Research #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2401.15699

Abstract

This paper studies properties of Γ-limits of Korevaar-Schoen p-energies on a Cheeger space. When p>1, this kind of limit provides a natural p-energy form that can be used to define a p-Laplacian, and whose domain is the Newtonian Sobolev space N^1,p. When p=1, the limit can be interpreted as a total variation functional whose domain is the space of BV functions. When the underlying space is compact, the Γ-convergence of the p-energies is improved to Mosco convergence for every p ≥ 1.

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