An approximation result for free discontinuity functionals by means of non-local energies
✍ Scribed by Luca Lussardi
- Publisher
- John Wiley and Sons
- Year
- 2008
- Tongue
- English
- Weight
- 133 KB
- Volume
- 31
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.1019
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✦ Synopsis
Abstract
We approximate, in the sense of Γ‐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 ϕ=Id is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non‐local energies. Copyright © 2008 John Wiley & Sons, Ltd.