A regularity theory for scalar local minimizers of splitting-type variational integrals

Abstract

Starting from Giaquinta\u27s counterexample [Gi] we introduce the class of splitting functionals being of (p,q)-growth with exponents pleq q<infty and show for the scalar case that locally bounded local minimizers are of class C^{1,mu}. Note that to our knowledge the only C^{1,mu}-results without imposing a relation between p and q concern the case of two independent variables as it is outlined in Marcellini\u27s paper [Ma1], Theorem A, and later on in the work of Fusco and Sbordone [FS], Theorem 4.2