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Characterization of optimal shapes and masses through Monge-Kantorovich equation

Characterization of optimal shapes and masses through Monge-Kantorovich equation We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of the European Mathematical Society Springer Journals

Characterization of optimal shapes and masses through Monge-Kantorovich equation

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Publisher
Springer Journals
Copyright
Copyright © 2000 by Springer-Verlag Berlin Heidelberg & EMS
Subject
Mathematics; Mathematics, general
ISSN
1435-9855
DOI
10.1007/s100970000027
Publisher site
See Article on Publisher Site

Abstract

We study some problems of optimal distribution of masses, and we show that they can be characterized by a suitable Monge-Kantorovich equation. In the case of scalar state functions, we show the equivalence with a mass transport problem, emphasizing its geometrical approach through geodesics. The case of elasticity, where the state function is vector valued, is also considered. In both cases some examples are presented.

Journal

Journal of the European Mathematical SocietySpringer Journals

Published: May 1, 2001

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