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INVERSE ITERATION FOR p-GROUND STATES
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).ORCID iD: 0000-0003-4309-9242
2016 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 144, no 5, 2121-2131 p.Article in journal (Refereed) PublishedText
Abstract [en]

We adapt the inverse iteration method for symmetric matrices to some nonlinear PDE eigenvalue problems. In particular, for p is an element of (1, infinity) and a given domain Omega subset of R-n, we analyze a scheme that allows us to approximate the smallest value the ratio integral(Omega)vertical bar D psi vertical bar(p)dx/ integral(Omega)vertical bar psi vertical bar(p)dx can assume for functions psi that vanish on partial derivative Omega. The scheme in question also provides a natural way to approximate minimizing psi. Our analysis also extends in the limit as p -> infinity and thereby fashions a new approximation method for ground states of the infinity Laplacian.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2016. Vol. 144, no 5, 2121-2131 p.
Keyword [en]
Nonlinear eigenvalue problem, p-Laplacian, inverse iteration, power method
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-184009DOI: 10.1090/proc/12860ISI: 000370723200026ScopusID: 2-s2.0-84958549975OAI: oai:DiVA.org:kth-184009DiVA: diva2:915373
Note

QC 20160330

Available from: 2016-03-30 Created: 2016-03-22 Last updated: 2016-03-30Bibliographically approved

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Lindgren, Erik
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