Partial regularity result for non-autonomous elliptic systems with general growth
Teresa Isernia, Chiara Leone, Anna Verde · Communications on Pure & Applied Analysis · 2021
In this paper we prove a partial Hölder regularity result for weak solutions \begin{document}$ u:\Omega\to \mathbb{R}^N $\end{document} , \begin{document}$ N\geq 2 $\end{document} , to non-autonomous elliptic systems with general growth of the type: \begin{document}$ \begin{equation*} -{\rm{div}} a(x, u, Du) = b(x, u, Du) \quad \;{\rm{ in }}\; \Omega. \end{equation*} $\end{document} The crucial point is that the operator \begin{document}$ a $\end{document} satisfies very weak regularity properties and a general growth, while the inhomogeneity \begin{document}$ b $\end{document} has a controllable growth.