Abstract

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 α\alpha-Hölder continuous for all α<1\alpha < 1.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

  • local minimizer
  • regularity
  • nonconvex functional

Mathematics Subject Classification

49N60, 35J20

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Suggested citation

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. https://doi.org/10.68381/jca1023

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Published by Heldermann Verlag, 2003. Rights now held by Banach Press LLC.