Calculus of Variations and Geometric Measure Theory

A. Braides - G. Dal Maso

Continuity of some non-local functionals with respect to a convergence of the underlying measures

created by braidesa on 04 Apr 2022
modified on 10 Dec 2023


Published Paper

Inserted: 4 apr 2022
Last Updated: 10 dec 2023

Journal: J. Math. Pures Appl.
Volume: 170
Pages: 136--149
Year: 2023
Doi: 10.1016/j.matpur.2022.12.005
Links: Springer view-only version


We study some non-local functionals on the Sobolev space $W^{1,p}_0(\Omega)$ involving a double integral on $\Omega\times\Omega$ with respect to a measure $\mu$. We introduce a suitable notion of convergence of measures on product spaces which implies a stability property in the sense of $\Gamma$-convergence of the corresponding functionals.

Keywords: Gamma-convergence, non-local functionals, graphons, cut norm