Article Contents
Article Contents

On non quasiconvex problems of the calculus of variations

• 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.

Mathematics Subject Classification: Primary: 49K20, 49K24.

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