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 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 the p-Laplace system, our conclusions broaden the range of the admissible values of the exponent p previously known. © 2021, The Author(s).

Authors
Balci A.K.1 , Cianchi A.2 , Diening L.1 , Maz’ya V. 3, 4
Publisher
Springer
Language
English
Status
Published
Year
2021
Organizations
  • 1 Fakultät für Mathematik, University Bielefeld, Universitätsstrasse 25, Bielefeld, 33615, Germany
  • 2 Dipartimento di Matematica e Informatica “U. Dini”, Università di Firenze, Viale Morgagni 67/A, Firenze, 50134, Italy
  • 3 Department of Mathematics, Linköping University, Linköping, 581 83, Sweden
  • 4 Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklay St, Moscow, 117198, Russian Federation
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