An approximation result for free discontinuity functionals by means of non‐local energies |
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Authors: | Luca Lussardi |
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Institution: | Dipartimento di Matematica, Facoltà di Ingegneria, Università degli Studi di Brescia, Via Valotti 9, 25133 Brescia, Italy |
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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 ?=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. |
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Keywords: | variational approximation free discontinuities variational problems in a geometric measure‐theoretic setting methods involving semicontinuity and convergence relaxation |
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