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
Approximation of the least Rayleigh quotient for degree p homogeneous funetionals
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-4309-9242
2017 (English)In: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 272, no 12, p. 4873-4918Article in journal (Refereed) Published
Abstract [en]

We present two novel methods for approximating minimizers of the abstract Rayleigh quotient Phi(u)/parallel to u parallel to(p). Here Phi is a strictly convex functional on a Banach space with norm parallel to center dot parallel to, and Phi is assumed to be positively homogeneous of degree p is an element of (1,infinity). Minimizers are shown to satisfy partial derivative Phi(u) - lambda j(p)(u) there exists 0 for a certain lambda is an element of R, where J(p) is the subdifferential of 1/p parallel to center dot parallel to(p.) The first approximation scheme is based on inverse iteration for square matrices and involves sequences that satisfy partial derivative Phi(u(k)) - j(p()u(k-1)) there exists 0 (k is an element of N) The second method is based on the large time behavior of solutions of the doubly nonlinear evolution j(p)((v) over circle (t)) + partial derivative Phi(v(t)) there exists 0 (a,e,t > 0) and more generally p -curves of maximal slope for Phi. We show that both schemes have the remarkable property that the Rayleigh quotient is nonincreasing along solutions and that properly scaled solutions converge to a minimizer of Phi(u)/parallel to u parallel to(p). These results are new even for Hilbert spaces and their primary application is in the approximation of optimal constants and extremal functions for inequalities in Sobolev spaces.

Place, publisher, year, edition, pages
ACADEMIC PRESS INC ELSEVIER SCIENCE , 2017. Vol. 272, no 12, p. 4873-4918
Keywords [en]
Nonlinear eigenvalue problem, Doubly nonlinear evolution, Inverse iteration, Large time behavior
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-207865DOI: 10.1016/j.jfa.2017.02.024ISI: 000400539700001Scopus ID: 2-s2.0-85015702520OAI: oai:DiVA.org:kth-207865DiVA, id: diva2:1103028
Note

QC 20170530

Available from: 2017-05-30 Created: 2017-05-30 Last updated: 2017-05-30Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Lindgren, Erik

Search in DiVA

By author/editor
Lindgren, Erik
By organisation
Mathematics (Div.)
In the same journal
Journal of Functional Analysis
Mathematical Analysis

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 9 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