On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators

  • We consider a Sturm-Liouville boundary value problem in a bounded domain D of R^n. By this is meant that the differential equation is given by a second order elliptic operator of divergent form in D and the boundary conditions are of Robin type on bD. The first order term of the boundary operator is the oblique derivative whose coefficients bear discontinuities of the first kind. Applying the method of weak perturbation of compact self-adjoint operators and the method of rays of minimal growth, we prove the completeness of root functions related to the boundary value problem in Lebesgue and Sobolev spaces of various types.

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Author:Alexander Shlapunov, Nikolai Tarkhanov
Series (Serial Number):Preprints des Instituts für Mathematik der Universität Potsdam (1(2012)11)
Document Type:Preprint
Date of Publication (online):2012/01/18
Year of Completion:2012
Publishing Institution:Universität Potsdam
Release Date:2012/01/18
Tag:Lipschitz domains; Sturm-Liouville problems; discontinuous Robin condition; root functions
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 / 35Bxx Qualitative properties of solutions / 35B25 Singular perturbations
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J60 Nonlinear elliptic 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-Notation: SI 990 , SK 540