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Existence of solutions for some implicit partial differential equations and applications to variational integrals involving quasi-affine functions

Published online by Cambridge University Press:  12 July 2007

Bernard Dacorogna  and
Ana Margarida Ribeiro
Bernard Dacorogna
Affiliation:
Institut de mathématiques, EPFL, 1015 Lausanne, Switzerland (bernard.dacorogna@epfl.ch; ana.ribeiro@epfl.ch)
Ana Margarida Ribeiro
Affiliation:
Institut de mathématiques, EPFL, 1015 Lausanne, Switzerland (bernard.dacorogna@epfl.ch; ana.ribeiro@epfl.ch)
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Abstract

We discuss some existence theorems for partial differential inclusions, subject to Dirichlet boundary conditions, of the form where Φ is a quasi-affine function and so, in particular, for Φ(Du) = det Du.

We then apply it to minimization problems of the form

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 5 , October 2004 , pp. 907 - 921
Copyright
Copyright © Royal Society of Edinburgh 2004

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