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Korean Mathematical Society JKMS

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J. Korean Math. Soc. 2010; 47(2): 331-350

Printed March 1, 2010

https://doi.org/10.4134/JKMS.2010.47.2.331

Copyright © The Korean Mathematical Society.

Young measures, Cartesian maps, and polyconvexity

Patrick Bernard and Ugo Bessi

Universit\'e Paris-Dauphine and Universit\`a di Roma 3

Abstract

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We consider the variational problem consisting of minimizing a polyconvex integrand for maps between manifolds. We offer a simple and direct proof of the existence of a minimizing map. The proof is based on Young measures.

Keywords: calculus of variations, polyconvexity, gradient measures

MSC numbers: 49Q20, 49J45

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