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An existence result for a nonconvex variational problem via regularity

Published online by Cambridge University Press:  15 September 2002

Irene Fonseca,
Nicola Fusco and
Paolo Marcellini
Irene Fonseca
Affiliation:
Carnegie-Mellon University, Pittsburgh, Pennsylvania 15213, U.S.A.; fonseca@andrew.cmu.edu.
Nicola Fusco
Affiliation:
Dipartimento di Matematica “R. Caccioppoli”, Università di Napoli, Via Cintia, 80126 Napoli, Italy; fusco@matna1.dma.unina.it.
Paolo Marcellini
Affiliation:
Dipartimento di Matematica “U. Dini”, Università di Firenze, Viale Morgagni 67 A, 50134 Firenze, Italy; marcell@udini.math.unifi.it.
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Abstract

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

Keywords

Nonconvex variational problemsuniform convexityregularityimplicit differential equations.

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 7 , 2002, pp. 69 - 95
Copyright
© EDP Sciences, SMAI, 2002

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