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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
Affiliation:
Institut de mathématiques, EPFL, 1015 Lausanne, Switzerland ([email protected]; [email protected])
Ana Margarida Ribeiro
Affiliation:
Institut de mathématiques, EPFL, 1015 Lausanne, Switzerland ([email protected]; [email protected])

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
Copyright
Copyright © Royal Society of Edinburgh 2004

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