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Singular perturbations of elliptic operators

  • We develop a new approach to the analysis of pseudodifferential operators with small parameter 'epsilon' in (0,1] on a compact smooth manifold X. The standard approach assumes action of operators in Sobolev spaces whose norms depend on 'epsilon'. Instead we consider the cylinder [0,1] x X over X and study pseudodifferential operators on the cylinder which act, by the very nature, on functions depending on 'epsilon' as well. The action in 'epsilon' reduces to multiplication by functions of this variable and does not include any differentiation. As but one result we mention asymptotic of solutions to singular perturbation problems for small values of 'epsilon'.

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Metadaten
Author:Evgueniya Dyachenko, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus-69502
ISSN:2193-6943
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (3 (2014) 1)
Publisher:Universitätsverlag Potsdam
Place of publication:Potsdam
Document Type:Preprint
Language:English
Year of first Publication:2014
Year of Completion:2014
Publishing Institution:Universität Potsdam
Publishing Institution:Universitätsverlag Potsdam
Release Date:2014/01/23
Tag:asymptotics; ellipticity with parameter; pseudodifferential operator; regularization; singular perturbation
Volume:3
Issue:1
Pagenumber:21
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Dxx Stability theory [See also 37C75, 93Dxx] / 34D15 Singular perturbations
34-XX ORDINARY DIFFERENTIAL EQUATIONS / 34Exx Asymptotic theory / 34E20 Singular perturbations, turning point theory, WKB methods
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Bxx Qualitative properties of solutions / 35B25 Singular perturbations
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2014
Publication Way:Universitätsverlag Potsdam
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht