Abstract
A Dirichlet region for an optimal mass transportation problem is, roughly speaking, a zone in which the transportation cost is vanishing. We study the optimal transportation problem with an unknown Dirichlet region Σ which varies in the class of closed connected subsets having prescribed 1-dimensional Hausdorff measure. We show the existence of an optimal Σ opt and study some of its geometrical properties. We also present numerical computations which show the shape of Σ opt in some model examples.
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Buttazzo, G., Oudet, E., Stepanov, E. (2002). Optimal Transportation Problems with Free Dirichlet Regions. In: dal Maso, G., Tomarelli, F. (eds) Variational Methods for Discontinuous Structures. Progress in Nonlinear Differential Equations and Their Applications, vol 51. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8193-7_4
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DOI: https://doi.org/10.1007/978-3-0348-8193-7_4
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9470-8
Online ISBN: 978-3-0348-8193-7
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