Abstract
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 a particular n-dimensional case is treated. Moreover, we investigate whether it is possible to approximate a given free discontinuity functional by means of non-local energies.
Lingua originale | English |
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pagine (da-a) | 2133-2146 |
Numero di pagine | 14 |
Rivista | Mathematical Methods in the Applied Sciences |
Volume | 31 |
DOI | |
Stato di pubblicazione | Pubblicato - 2008 |
Pubblicato esternamente | Sì |
Keywords
- free discontinuities
- variational convergence