A pointwise differential inequality and second-order regularity for nonlinear elliptic systems

A sharp pointwise differential inequality for vectorial second-order partial differential operators, with Uhlenbeck structure, is offered. As a consequence, optimal second-order regularity properties of solutions to nonlinear elliptic systems in domains in $${\mathbb R^n}$$ are derived. Both local and global estimates are established. Minimal assumptions on the boundary of the domain are required for the latter. In the special case of the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known.