liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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
2017 (English)In: Communications on Pure and Applied Mathematics, ISSN 0010-3640, E-ISSN 1097-0312, Vol. 70, no 7, 1316-1365 p.Article in journal (Refereed) Published
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
2017. Vol. 70, no 7, 1316-1365 p.
Keyword [en]
Elliptic equations, Carleson measures, Boundary value problems, Lipschitz domains
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:liu:diva-125452DOI: 10.1002/cpa.21649ISI: 000401720800003OAI: oai:DiVA.org:liu-125452DiVA: diva2:906300
Note

Funding agencies: Engineering and Physical Sciences Research Council [EP/J017450/1]; National Science Foundation DMS Grant [0901139]; CANPDE

Available from: 2016-02-24 Created: 2016-02-24 Last updated: 2017-06-13

Open Access in DiVA

No full text

Other links

Publisher's full text

Search in DiVA

By author/editor
Rule, David
By organisation
Mathematics and Applied MathematicsFaculty of Science & Engineering
In the same journal
Communications on Pure and Applied Mathematics
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

Altmetric score

Total: 992 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf