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 R n are derived. Both local and global esti...

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Bibliographic Details
Published in:Mathematische annalen 2022, Vol.383 (3-4), p.1-50
Main Authors: Balci, Anna Kh, Cianchi, Andrea, Diening, Lars, Maz’ya, Vladimir
Format: Article
Language:English
Subjects:
Differential equations
Domains
Mathematics
Mathematics and Statistics
Nonlinear systems
Operators (mathematics)
Regularity
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Summary: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.
ISSN:0025-5831
1432-1807
1432-1807
DOI:10.1007/s00208-021-02249-9