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arXiv · 2102.09423

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

Anna Kh. Balci·Andrea Cianchi·Lars Diening·Vladimir Maz'ya
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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 $\mathbb{R}^n$ 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.

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Anna Kh. Balci, Andrea Cianchi, Lars Diening, Vladimir Maz'ya. 2021-02-18. A pointwise differential inequality and second-order regularity for nonlinear elliptic systems. https://arxiv.org/abs/2102.09423

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