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
Asymptotics for solutions of elliptic equations in double divergence form
Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
North Eastern University.
2007 (English)In: Communications in Partial Differential Equations, ISSN 0360-5302, Vol. 32, no 2, 191-207 p.Article in journal (Refereed) Published
Abstract [en]

We consider weak solutions of an elliptic equation of the form ∂i∂i(aiju) = 0 and their asymptotic properties at an interior point. We assume that the coefficients are bounded, measurable, complex-valued functions that stabilize as x → 0 in that the norm of the matrix (aij(x) - δij) on the annulus B2r\Br is bounded by a function Ω(r), where Ω2(r) satisfies the Dini condition at r = 0, as well as some technical monotonicity conditions, under these assumptions, solutions need not be continuous. Our main result is an explicit formula for the leading asymptotic term for solutions with at most a mild singularity at x = 0. As a consequence, we obtain upper and lower estimates for the Lp-norm of solutions, as well as necessary and sufficient conditions for solutions to be bounded or tend to zero in Lp-mean as r → 0. Copyright © Taylor & Francis Group, LLC.

Place, publisher, year, edition, pages
2007. Vol. 32, no 2, 191-207 p.
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-40052DOI: 10.1080/03605300601113019Local ID: 52192OAI: oai:DiVA.org:liu-40052DiVA: diva2:260901
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-11

Open Access in DiVA

No full text

Other links

Publisher's full text

Authority records BETA

Maz´ya, Vladimir G.

Search in DiVA

By author/editor
Maz´ya, Vladimir G.
By organisation
The Institute of TechnologyApplied Mathematics
In the same journal
Communications in Partial Differential Equations
Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 299 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