Asymptotically regular operators in generalized Morrey spaces

Abstract

We obtain Calderón-Zygmund type estimates in generalized Morrey spaces for nonlinear equations of $p$-Laplacian type. Our result is obtained under minimal regularity assumptions both on the operator and on the domain. This result allows us to study asymptotically regular operators. As a byproduct, we obtain also generalized Hölder regularity of the solutions under some minimal restrictions of the weight functions.

10 pages

Cited by in corpus (2)

• Precise Morrey regularity of the weak solutions to a kind of quasilinear systems with discontinuous data
• Boundedness of the solutions of a kind of nonlinear parabolic systems