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 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.
Funding Agencies|Universita degli Studi di Firenze within the CRUI-CARE Agreement; Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)German Research Foundation (DFG) [SFB 1283/2 2021 - 317210226]; Research Project of the Italian Ministry of Education, University and Research (MIUR) Prin 2017 "Direct and inverse problems for partial differential equations: theoretical aspects and applications" [201758MTR2]; GNAMPA of the Italian INdAM - National Institute of High MathematicsIstituto Nazionale di Alta Matematica (INDAM); RUDN University Strategic Academic Leadership Program