The method of Fischer-Riesz equations for elliptic boundary value problems

  • We develop the method of Fischer-Riesz equations for general boundary value problems elliptic in the sense of Douglis-Nirenberg. To this end we reduce them to a boundary problem for a (possibly overdetermined) first order system whose classical symbol has a left inverse. For such a problem there is a uniquely determined boundary value problem which is adjoint to the given one with respect to the Green formula. On using a well elaborated theory of approximation by solutions of the adjoint problem, we find the Cauchy data of solutions of our problem.

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Metadaten
Author:Ammar Alsaedy, Nikolai Tarkhanov
URN:urn:nbn:de:kobv:517-opus-61792
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)24)
Document Type:Preprint
Language:English
Date of Publication (online):2012/09/20
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/09/20
Tag:Boundary value problems for first order systems; Fischer-Riesz equations; Green formula; regularisation
Organizational units:Mathematisch-Naturwissenschaftliche Fakultät / Institut für Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
MSC Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Fxx General first-order equations and systems / 35F45 Boundary value problems for linear first-order systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J56 Boundary value problems for first-order elliptic systems
47-XX OPERATOR THEORY / 47Nxx Miscellaneous applications of operator theory [See also 46Nxx] / 47N20 Applications to differential and integral equations
Collections:Universität Potsdam / Schriftenreihen / Preprints des Instituts für Mathematik der Universität Potsdam, ISSN 2193-6943 / 2012
Licence (German):License LogoKeine Nutzungslizenz vergeben - es gilt das deutsche Urheberrecht
Notes extern:RVK-Klassifikation: SI 990