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Boundary value problems for second order elliptic operators satisfying a Carleson condition
School of Mathematics Edinburgh University Mayfield Road Edinburgh, EH9 3JZ, UK.
Brown University Mathematics Department Providence, RI 02912, USA.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-8976-8299
2015 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312Article in journal (Refereed) Epub ahead of print
Abstract [en]

Let be a Lipschitz domain in Rn n ≥ 2, and L = divA∇· be a second order elliptic operator in divergence form. We establish solvability of the Dirichlet regularity problem with boundary data in H1,p(@) and of the Neumann problem with Lp(@) data for the operator L on Lipschitz domains with small Lipschitz con- stant. We allow the coefficients of the operator L to be rough obeying a certain Carleson condition with small norm. These results complete the results of [7] where the Lp(@) Dirichlet problem was considered under the same assumptions and [8] where the regularity and Neumann problems were considered on two dimensional domains.

Place, publisher, year, edition, pages
2015.
Keyword [en]
Elliptic equations, Carleson measures, Boundary value problems, Lipschitz domains
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-125452DOI: 10.1002/cpa.21649OAI: oai:DiVA.org:liu-125452DiVA: diva2:906300
Available from: 2016-02-24 Created: 2016-02-24 Last updated: 2016-08-19

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Rule, David
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