# American Institute of Mathematical Sciences

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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