On non quasiconvex problems of the calculus of variations
Bernard Dacorogna, Giovanni Pisante, Ana Margarida Ribeiro · Discrete and Continuous Dynamical Systems · 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.