An existence result for a nonconvex variational problem via regularity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 69-95.

Local Lipschitz continuity of minimizers of certain integrals of the Calculus of Variations is obtained when the integrands are convex with respect to the gradient variable, but are not necessarily uniformly convex. In turn, these regularity results entail existence of minimizers of variational problems with non-homogeneous integrands nonconvex with respect to the gradient variable. The $x$-dependence, explicitly appearing in the integrands, adds significant technical difficulties in the proof.

DOI : https://doi.org/10.1051/cocv:2002004
Classification : 49J45,  49K20,  35F30,  35R70
Mots clés : nonconvex variational problems, uniform convexity, regularity, implicit differential equations
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Fonseca, Irene; Fusco, Nicola; Marcellini, Paolo. An existence result for a nonconvex variational problem via regularity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 69-95. doi : 10.1051/cocv:2002004. http://www.numdam.org/articles/10.1051/cocv:2002004/

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