Asymptotically regular operators in generalized Morrey spaces

2019/04/24 by Byun, Sun-Sig, Softova, Lubomira · 2 citations
#35J60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1904.10713

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.

Cited by

• Optimal Sobolev embeddings for generalized Lorentz-Zygmund spaces
• Approximation of the Solutions to Quasilinear Parabolic Problems with Perturbed VMO_x Coefficients

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