Published Paper

Inserted: 5 jul 2023

Journal: The Quarterly Journal of Mathematics
Volume: 74
Number: 1
Pages: 273–299
Year: 2023
Doi: https://doi.org/10.1093/qmath/haac022
Links: Published version

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 $n \geq 3$.