Asymptotically regular operators in generalized Morrey spaces

Abstract

We obtain Calderón–Zygmund-type estimates in generalized Morrey spaces L q , φ ( Ω ) for nonlinear equations of p-Laplacian type. Our result is obtained under minimal regularity assumptions on both the operator and the domain Ω. This result allows us to study more general class of nonlinear equations which are asymptotically regular, that is, ‘near’ enough to some nonlinear operator of p-Laplacian type. As a by-product, we obtain also generalized Hölder regularity C 0 , φ ( Ω ) of the solution under some restrictions on the generalizing function φ.