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 the n-dimensional Euclidean space 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.

A pointwise differential inequality and second-order regularity for nonlinear elliptic systems / Anna Kh. Balci, Andrea Cianchi, Lars Diening, Vladimir Maz’ya. - In: MATHEMATISCHE ANNALEN. - ISSN 0025-5831. - STAMPA. - 383:(2022), pp. 1775-1824. [10.1007/s00208-021-02249-9]

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

Andrea Cianchi
;
2022

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 the n-dimensional Euclidean space 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.
383
1775
1824
Anna Kh. Balci, Andrea Cianchi, Lars Diening, Vladimir Maz’ya
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1287672
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