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.

Lussardi, L., An approximation result for free discontinuity functionals by means of non-local energies, <<MATHEMATICAL METHODS IN THE APPLIED SCIENCES>>, 2008; 31 (18): 2133-2146. [doi:10.1002/mma.1019] [http://hdl.handle.net/10807/1978]

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

Lussardi, Luca
2008

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.
2008
Inglese
Lussardi, L., An approximation result for free discontinuity functionals by means of non-local energies, <<MATHEMATICAL METHODS IN THE APPLIED SCIENCES>>, 2008; 31 (18): 2133-2146. [doi:10.1002/mma.1019] [http://hdl.handle.net/10807/1978]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/1978
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