Regularity for minimizers of functionals with nonstandard growth by $A$-harmonic approximation

Abstract

We prove partial regularity for minimizers of quasiconvex functionals of the type ${\int }_{\Omega }f(x,Du)dx$ with $p(x)$ growth with respect to the second variable. The proof is direct and uses a method of $A$-harmonic approximation.

23 pages