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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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