Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
Dense subsets of L-1-solutions to linear elliptic partial differential equations
KTH, Superseded Departments, Mathematics.ORCID iD: 0000-0002-1316-7913
2000 (English)In: Journal of Approximation Theory, ISSN 0021-9045, E-ISSN 1096-0430, Vol. 102, no 2, 189-216 p.Article in journal (Refereed) Published
Abstract [en]

Let Omega subset of R-N ( N greater than or equal to 2) be an unbounded domain, and L-m be a homogeneous linear elliptic partial differential operator with constant coefficients. In this paper we show, among other things, that rapidly decreasing L-1-solutions to L-m (in Omega) approximate all L-1-solutions to L-m (in Omega), provided there exist real numbers R-j --> infinity, epsilon greater than or equal to 0, and it sequence {y(j)} such that B(y(j), epsilon) boolean AND Omega = circle divide and \A(y(j), R-j, R-N\Omega)\/R-j(N) > epsilon For All j, where \.\ means the volume and [GRAPHICS] for z is an element of R-N, R > 0 and D subset of R-N. For m = 2, we can replace the volume density by the capacity-density. It appears that the problem is related to this characterization of largest sets on which a nonzero polynomial solution to L-m may vanish, along with its (m-1)-derivarives. We also study a similar approximation problem for polyanalytic functions in C.

Place, publisher, year, edition, pages
2000. Vol. 102, no 2, 189-216 p.
Keyword [en]
polyanalytic functions, higher order elliptic pde, L-1-approximation, dense subsets, quadrature domains, potential-theory
Identifiers
URN: urn:nbn:se:kth:diva-19591ISI: 000085604000002OAI: oai:DiVA.org:kth-19591DiVA: diva2:338283
Note
QC 20100525Available from: 2010-08-10 Created: 2010-08-10Bibliographically approved

Open Access in DiVA

No full text

Authority records BETA

Shahgholian, Henrik

Search in DiVA

By author/editor
Shahgholian, Henrik
By organisation
Mathematics
In the same journal
Journal of Approximation Theory

Search outside of DiVA

GoogleGoogle Scholar

urn-nbn

Altmetric score

urn-nbn
Total: 24 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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