Geodesic
BV Functions with Respect to a Measure and Relaxation of Metric Integral Functionals
Journal of convex analysis, Tome 6 (1999) no. 2, pp. 349-366.

Voir la notice de l'article provenant de la source Heldermann Verlag

We introduce and study the space of bounded variation functions with respect to a Radon measure μ on RN and to a metric integrand ϕ on the tangent bundle to μ. We show that it is equivalent to view such space as the class of μ-integrable functions for which a distributional notion of (μ, ϕ)-total variation is finite, or as the finiteness domain of a relaxed functional. We prove a quite, general coarea-type formula and then we focus our attention to the problem of finding an integral representation for the (μ, ϕ)-total variation.
Classification : 26A25, 49M20, 46N10
Mots-clés : Bounded variation functions, Radon measures, relaxation, duality, integral representation 
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     author = {G. Bellettini and G. Bouchitt\'e and I. Fragal\`a},
     title = {BV {Functions} with {Respect} to a {Measure} and {Relaxation} of {Metric} {Integral} {Functionals}},
     journal = {Journal of convex analysis},
     pages = {349--366},
     publisher = {mathdoc},
     volume = {6},
     number = {2},
     year = {1999},
     url = {http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a6/}
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G. Bellettini; G. Bouchitté; I. Fragalà. BV Functions with Respect to a Measure and Relaxation of Metric Integral Functionals. Journal of convex analysis, Tome 6 (1999) no. 2, pp. 349-366. http://geodesic.mathdoc.fr/item/JCA_1999_6_2_JCA_1999_6_2_a6/