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Regularity properties for Monge transport density and for solutions of some shape optimization problem

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Abstract.

In this paper we study the dimension of some measures which are related to the classical Monge's optimal mass transport problem and are solutions of a scalar shape optimization problem. Moreover in the case of maximal dimension we will study the summability of the associate densities.

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Authors and Affiliations

  1. Dipartimento di Matematica Applicata, Università di Pisa, via Bonanno Pisano 25/B, 56127 Pisa, Italy (e-mail: depascal@dm.unipi.it) , , , , , , IT

    Luigi De Pascale

  2. Scuola Normale Superiore, Piazza dei Cavalieri 7, 56127 Pisa, Italy (e-mail:pratelli@cibs.sns.it) , , , , , , IT

    Aldo Pratelli

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  1. Luigi De Pascale
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  2. Aldo Pratelli
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Received: 16 November 2000 / Accepted: 4 December 2000 / Published online: 18 January 2002

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De Pascale, L., Pratelli, A. Regularity properties for Monge transport density and for solutions of some shape optimization problem. Calc Var 14, 249–274 (2002). https://doi.org/10.1007/s005260100086

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  • DOI: https://doi.org/10.1007/s005260100086

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