Sobolev regularity for linear growth functionals acting on ℂ-elliptic operators

Abstract

Abstract In this paper, we prove the higher Sobolev regularity of minimizers for convex integral functionals evaluated on linear differential operators of order one. This work intends to generalize the already existing theory for the cases of full and symmetric gradients to the entire class of ${\mathbb C}$-elliptic operators therein including the trace-free symmetric gradient for dimension $n \geq 3$.