The conormal and Robin boundary value problems in nonsmooth domains satisfying a measure condition

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Author(s)

Detail(s)

Original languageEnglish
Article number109167
Number of pages32
Journal / PublicationJournal of Functional Analysis
Volume281
Issue number9
Online published30 Jun 2021
Publication statusPublished - 1 Nov 2021
Externally publishedYes

Abstract

We consider elliptic equations and systems in divergence form with the conormal or the Robin boundary conditions, with small BMO (bounded mean oscillation) or variably partially small BMO coefficients. We propose a new class of domains which are locally close to a half space (or convex domains) with respect to the Lebesgue measure in the system (or scalar, respectively) case, and obtain the Wp1 estimate for the conormal problem with the homogeneous boundary condition. Such condition is weaker than the Reifenberg flatness condition, for which the closeness is measured in terms of the Hausdorff distance, and the semi-convexity condition. For the conormal problem with inhomogeneous boundary conditions, we also assume that the domain is Lipschitz. By using these results, we obtain the Wp1 and weighted Wp1 estimates for the Robin problem in these domains. © 2021 Published by Elsevier Inc.

Research Area(s)

  • The conormal and Robin problems, BMO coefficients, Nonsmooth domains, Muckenhoupt weights