Sobolev–Zygmund solutions for nonlinear elliptic equations with growth coefficients in BMO

Abstract

In this paper we study, in the setting of the Zygmund–Sobolev spaces, weak solutions to Dirichlet problems for nonlinear elliptic equations in divergence form with unbounded coefficients of the type $$\begin{aligned} {\text {div}}\;({\mathcal {A}}(x,\nabla u)+{\mathcal {B}}(x,u)) = {\text {div}}\;{\mathcal {F}} \end{aligned}$$ in a bounded Lipschitz domain $$\Omega \subset {{\mathbb {R}}}^{N}$$ , $$N>2$$ .