Mixed local and nonlocal equations with measure data (Q2093431)

This article discusses some general elliptic problems of the type \(-\operatorname{div}A(x, Du)+\mathcal{L} u=\mu\) in a bounded domain \(\Omega\subset\mathbb{R}^n\), \(n\geq 2\). Here \(\operatorname{div}A(x, Du)\) is a quasilinear elliptic operator that extends the \(p\)-Laplace operator while \(\mathcal{L}u\) is a nonlocal operator. The authors establish existence, regularity and Wolff potential estimates for solutions. As a consequence, Calderón-Zygmund type estimates and continuity criteria for solutions are deduced.