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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.

Identiferoai:union.ndltd.org:Potsdam/oai:kobv.de-opus-ubp:5775
Date January 2012
CreatorsShlapunov, Alexander, Tarkhanov, Nikolai
PublisherUniversität Potsdam, Mathematisch-Naturwissenschaftliche Fakultät. Institut für Mathematik
Source SetsPotsdam University
LanguageEnglish
Detected LanguageEnglish
TypePreprint
Formatapplication/pdf
Rightshttp://opus.kobv.de/ubp/doku/urheberrecht.php

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