Published Paper

Inserted: 1 jul 2026
Last Updated: 1 jul 2026

Journal: Ricerche di Matematica
Year: 2026
Doi: https://doi.org/10.1007/s11587-026-01148-y

Abstract:

The aim of this paper is to derive some Calderòn-Zygmund estimates for local solutions $u$ of nonlinear elliptic systems of the type \[ {\rm div}\mathbf{A}(x, Du) = {\rm div}
\mathbf{G}
^{p - 2}\mathbf{G} \qquad {\rm in} \quad \Omega \subset \mathbb{R}^n, \] where $\Omega \subset \mathbb{R}^n$ is a bounded domain. We assume that $u : \Omega \to \mathbb{R}^N$ belongs to a weighted Sobolev space $W_{loc}^{1, p}$, with $p \in \left(\frac{2n}{n + 2}, 2\right)$, $\mathbf{G}$ belongs to a weighted $L_{loc}^{p}$ space and $x \to \mathbf{A}(x, \xi)$ has growth coefficients in the John and Nirenberg space $BMO$.
As an application of similar techniques, we also consider weak solutions $u$ of linear elliptic systems of the type \[ {\rm div}(A(x)Du) = {\rm div}\, G, \] where the matrix $A(x)$ lies in the space $BMO$. In this case, an improvement of the admissible exponent range in the Calderòn-Zygmund estimate is obtained.