An approximation result for free discontinuity functionals by means of non-local energies

被引：2

作者：

Lussardi, Luca ^{[1
]}

机构：

[1] Univ Brescia, Dipartimento Matemat, Fac Ingn, I-25133 Brescia, Italy

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2008年 / 31卷 / 18期

关键词：

variational approximation; free discontinuities; variational problems in a geometric measure-theoretic setting; methods involving semicontinuity and convergence; relaxation;

D O I：

10.1002/mma.1019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We approximate, in the sense of Gamma-convergence, free discontinuity functionals with linear growth by a sequence of non-local integral functionals depending on the average of the gradient on small balls. The result extends to a higher dimension what is already proved in (Ann. Mat. Pura Appl. 2007; 186(4): 722-744), where there is the proof of the general one-dimensional case and in (ESAIM Control Optim. Calc. Var. 2007; 13(1):135-162), where the n-dimensional case with phi=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies. Copyright (C) 2008 John Wiley & Sons, Ltd.

引用

页码：2133 / 2146

页数：14

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