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.
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GC
Giovanni Cupini
Dip. di Matematica, Università di Firenze, Viale Morgagni 67/A, 50134 Firenze, Italy
G. Cupini, A. P. Migliorini. “Hölder Continuity for Local Minimizers of a Nonconvex Variational Problem.” Journal of Convex Analysis 10 (2003), No. 2, 389–408.