Calculus of Variations and Geometric Measure Theory

A. Braides - G. Dal Maso

Compactness for a class of integral functionals with interacting local and non-local terms

created by braidesa on 22 Dec 2022
modified on 12 Jul 2023


Published Paper

Inserted: 22 dec 2022
Last Updated: 12 jul 2023

Journal: Calc. Var. Partial Differential Equations
Volume: 62
Number: 148
Year: 2023
Doi: 10.1007/s00526-023-02491-w


We prove a compactness result with respect to Γ-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the Γ-limit depends on the interaction between the local and non-local terms of the converging subsequence. The result is applied to concentration and homogenization problems.