2000/06/08 by Massimo Gobbino, Maria Giovanna Mora, Gobbino, Massimo +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations #math.FA
paper · pdf · doi:10.48550/arxiv.math/0006059
39 pages. to appear on Proc. Royal Soc. Edinb. Ser. A
arxiv created 2000/06/08 · openalex publication_date 2000/06/08 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We approximate functionals depending on the gradient of u and on the behaviour of u near the discontinuity points, by families of non-local functionals where the gradient is replaced by finite differences. We prove pointwise convergence, Γ-convergence, and a compactness result which implies, in particular, the convergence of minima and minimizers.