Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-28T02:32:28.774Z Has data issue: false hasContentIssue false

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)