Abstract
AbstractA 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 $${\mathbb R^n}$$
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.
Funder
Deutsche Forschungsgemeinschaft
Ministero dell’Istruzione, dell’Universitá e della Ricerca
Gruppo Nazionale per l’Analisi Matematica, la Probabilitá e le loro Applicazioni
RUDN University
Publisher
Springer Science and Business Media LLC
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