| Abstract: |
| We present an overview of several regularity results for specific classes of elliptic systems established in recent years. Specifically, employing the Einstein summation convention, we investigate the following system:
\[
\left\{\begin{aligned} &u\in\W\\ & -\Di \, A_i^\nu(x, u, \DD u)=-\Di\big(E_{i}(x) \, u^{\nu}\big)+f^\nu(x), \quad \text{$x\in\Om$}, \, \nu=1, \ldots N \end{aligned}\right.
\]
defined on a domain $\Om \subset \R^n$ ($n \geq 3$, $N \geq 2$), where $A_i^{\nu}$ and $E_i(x)$ are required to satisfy appropriate structural and integrability conditions. The analysis further assumes that the data $f^{\nu}$ belong to the Lebesgue space $L^{t}(\Om)$ for $\nu=1, \ldots, N$, with $t \geq \dfrac{2n}{n+2}$. |
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