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Journal of Convex Analysis 10 (2003), No. 2, 389--408
Copyright Heldermann Verlag 2003

Hölder Continuity for Local Minimizers of a Nonconvex Variational Problem

Giovanni Cupini
Dip. di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy, cupini@math.unifi.it

Anna Paola Migliorini
Dip. di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy, amiglior@math.unifi.it

We consider integral functionals of the Calculus of Variations where the energy density is a continuous function with p-growth, p > 1, uniformly convex at infinity with respect to the gradient variable. We prove that local minimizers are a-Hölder continuous for all a < 1.

Keywords: local minimizer, regularity, nonconvex functional.

MSC 1991: 49N60, 35J20.

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