In this paper we introduce a definition of BV based on measure upper gradients and prove the equivalence of this definition, and the coincidence of the corresponding notions of total variation, with the definitions based on relaxation of L1 norm of the slope of Lipschitz functions or upper gradients. As in the previous work by the first author...
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2014 (v1)PublicationUploaded on: April 14, 2023
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2019 (v1)Publication
We provide sharp conditions for the finiteness and the continuity of multimarginal optimal transport with repulsive cost, expressed in terms of a suitable concentration property of the measure. To achieve this result, we analyze the Kantorovich potentials of the optimal plans, and we estimate the distance of any optimal plan from the regions...
Uploaded on: April 14, 2023 -
2015 (v1)Publication
We study a multimarginal optimal transportation problem in one dimension. For a symmetric, repulsive cost function, we show that given a minimizing transport plan, its symmetrization is induced by a cyclical map, and that the symmetric optimal plan is unique. The class of costs that we consider includes, in particular, the Coulomb cost, whose...
Uploaded on: April 14, 2023