Mixed local and nonlocal equations with measure data
type: Item
instance of: scholarly article
title: Mixed local and nonlocal equations with measure data
author: Sun-Sig Byun
author: Kyeong Song
published in: Calculus of Variations and Partial Differential Equations
publication date: 2022-11-08T00:00:00Z
review text: This article discusses some general elliptic problems of the type \(-\operatorname{div}A(x, Du)+\mathcal{L} u=\mu\) in a bounded domain \(\Omega\subset\mathbb{R}^n\), \(n\geq 2\). Here \(\operatorname{div}A(x, Du)\) is a quasilinear elliptic operator that extends the \(p\)-Laplace operator while \(\mathcal{L}u\) is a nonlocal operator. The authors establish existence, regularity and Wolff potential estimates for solutions. As a consequence, Calderón-Zygmund type estimates and continuity criteria for solutions are deduced.
reviewed by: Marius Ghergu
Mathematics Subject Classification ID: 31C45
Mathematics Subject Classification ID: 35A01
Mathematics Subject Classification ID: 35B65
Mathematics Subject Classification ID: 35R06
zbMATH DE Number: 7613194
zbMATH Keywords: elliptic equations
zbMATH Keywords: local and nonlocal operators
zbMATH Keywords: measure data
MaRDI profile type: Publication
full work available at URL: s00526-022-02349-7
OpenAlex ID: W4308178015
Wikidata QID: Q115385859
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DOI: 10.1007/S00526-022-02349-7
description: scientific article; zbMATH DE number 7613194