A pointwise differential inequality and second-order regularity for nonlinear elliptic systems
Anna Kh. Balci, Andrea Cianchi, Lars Diening, Vladimir Gilelevich Maz'ya · Mathematische Annalen · 2021
Abstract 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 $${\mathbb R^n}$$ Rn 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 thep-Laplace system, our conclusions broaden the range of the admissible values of the exponentppreviously known.