July  2005, 13(4): 961-983. doi: 10.3934/dcds.2005.13.961

On non quasiconvex problems of the calculus of variations

1. 

Department of Mathématics, EPFL, 1015 Lausanne

2. 

School of Mathematics, Georgia Tech, 30332, Atlanta, GA, United States

3. 

Section of Mathematics, EPFL, 1015 Lausanne, Switzerland

Received  September 2004 Revised  March 2005 Published  August 2005

We study existence of minimizers for problems of the type

inf{$\int_\Omega f(Du(x)) dx:u=u_{\xi _0}$ on $\partial\Omega$ }

where $f$ is non quasiconvex and $u_{\xi_0}$ is an affine function. Applying some new results on differential inclusions, we get sufficient conditions. We also study necessary conditions. We then consider some examples.

Citation: Bernard Dacorogna, Giovanni Pisante, Ana Margarida Ribeiro. On non quasiconvex problems of the calculus of variations. Discrete and Continuous Dynamical Systems, 2005, 13 (4) : 961-983. doi: 10.3934/dcds.2005.13.961
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