A notion of total variation depending on a metric with discontinuous coefficients
M. Amar
Dipartimento di Matematica, Università di Pavia, 27100 Pavia, Italy; International School for Advanced Studies SISSA/ISAS, 34014 Trieste, ItalyG. Bellettini
Dipartimento di Matematica, Università di Bologna, 40127 Bologna, Italy; International School for Advanced Studies SISSA/ISAS, 34014 Trieste, Italy
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Abstract
Given a function , we introduce a notion of total variation of depending on a possibly discontinuous Finsler metric. We prove some integral representation results for this total variation, and we study the connections with the theory of relaxation.
Résumé
Étant donnée une fonction , on définit une notion de variation totale de , dépendant d’une métrique Finslérienne discontinue. On démontre quelques résultats de représentation intégrale pour cette variation totale et ses relations avec la théorie de la relaxation.
Cite this article
M. Amar, G. Bellettini, A notion of total variation depending on a metric with discontinuous coefficients. Ann. Inst. H. Poincaré Anal. Non Linéaire 11 (1994), no. 1, pp. 91–133
DOI 10.1016/S0294-1449(16)30197-4