Convex variational integrals with a wide range of anisotropy. - Part II : Mixed linear/superlinear growth conditions

Abstract

We propose the study of variational integrands with mixed anisotropic linear/superlinear growth conditions, i.e. of energy densities with mixed "plastic/elastic" behavior. A class of variational problems satysfying this new kind of growth condition is introduced, and some recent regularity results (see [Bi1] and [BF6]) are applied to prove uniqueness (up to a constant) and local C^{1,\alpha}-regularity of generalized minimizers.