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The Neumann problem after Spencer

  • When trying to extend the Hodge theory for elliptic complexes on compact closed manifolds to the case of compact manifolds with boundary one is led to a boundary value problem for the Laplacian of the complex which is usually referred to as Neumann problem. We study the Neumann problem for a larger class of sequences of differential operators on a compact manifold with boundary. These are sequences of small curvature, i.e., bearing the property that the composition of any two neighbouring operators has order less than two.

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Metadaten
Author details:Azal Mera, Nikolai Nikolaevich TarkhanovORCiDGND
URN:urn:nbn:de:kobv:517-opus4-90631
ISSN:2193-6943
Publication series (Volume number):Preprints des Instituts für Mathematik der Universität Potsdam (5 (2016) 6)
Publisher:Universitätsverlag Potsdam
Place of publishing:Potsdam
Publication type:Preprint
Language:English
Year of first publication:2016
Publication year:2016
Publishing institution:Universität Potsdam
Publishing institution:Universitätsverlag Potsdam
Release date:2016/05/17
Tag:Hodge theory; Neumann problem; elliptic complex; manifold with boundary
Volume:5
Issue:6
Number of pages:21
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
DDC classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Nxx Overdetermined systems [See also 58Hxx, 58J10, 58J15] / 35N15 @-Neumann problem and generalizations; formal complexes [See also 32W05, 32W10, 58J10]
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Jxx Partial differential equations on manifolds; differential operators [See also 32Wxx, 35-XX, 53Cxx] / 58J10 Differential complexes [See also 35Nxx]; elliptic complexes
Publishing method:Universitätsverlag Potsdam
Collection(s):Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2016
License (German):License LogoKeine öffentliche Lizenz: Unter Urheberrechtsschutz
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