Partial regularity for elliptic systems with critical growth
Teresa Isernia, Chiara Leone, Anna Verde · Rendiconti Lincei Matematica e Applicazioni · 2022
We prove a partial Hölder regularity result for weak solutions u:\Omega\to\mathbb{R}^N , N\geq 2 , to non-autonomous elliptic systems with general growth of the type -\operatorname{div} a(x, u, Du) = b(x, u, Du)\quad\text{in }\Omega. The crucial point is that the operator a satisfies very weak regularity properties and general growth, while for the inhomogeneity b we allow a critical growth condition.