Asymptotically regular operators in generalized Morrey spaces

Sun-Sig Byun, Lubomira Softova

Published 2019-04-24Version 1

We obtain Calder\'on-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 H\"older regularity of the solutions under some minimal restrictions of the weight functions.