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

2022/04/04 by Andrea Braides, Gianni Dal Maso, Braides, Andrea +1
Computer Science · Mathematics · #28A33 #28A35 #46E35 #49J45 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2204.01552

openalex publication_date 2022/04/04 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28

Abstract

We study some non-local functionals on the Sobolev space W^1,p₀(Ω) involving a double integral on Ω×Ω with respect to a measure μ. We introduce a suitable notion of convergence of measures on product spaces which implies a stability property in the sense of Γ-convergence of the corresponding functionals.

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