Calculus of Variations and Geometric Measure Theory

G. Cupini - A. P. Migliorini

Hölder continuity for local minimizers of a nonconvex variational problem

created on 12 Dec 2002
modified on 10 Dec 2003


Published Paper

Inserted: 12 dec 2002
Last Updated: 10 dec 2003

Journal: J. Convex Anal.
Volume: 10
Number: 2
Pages: 389-408
Year: 2003


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 $\alpha$ Hölder continuous for all $\alpha<1$.

Keywords: regularity, Local minimizer, nonconvex functional