TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - Sturm-Liouville problems in domains with non-smooth edges
N2  - We consider a (generally, non-coercive) mixed boundary value problem in a bounded domain for a second order elliptic differential operator A. The differential operator is assumed to be of divergent form and the boundary operator B is of Robin type. The boundary is assumed to be a Lipschitz surface. Besides, we distinguish a closed subset of the boundary and control the growth of solutions near this set. We prove that the pair (A,B) induces a Fredholm operator L in suitable weighted spaces of Sobolev type, the weight function being a power of the distance to the singular set. Moreover, we prove the completeness of root functions related to L.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 2(2013)13 
KW  - Second order elliptic equations
KW  - non-coercive boundary conditions
KW  - root functions
KW  - weighted spaces
Y1  - 2013
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-67336
ER  - 
TY  - INPR
A1  - Shlapunov, Alexander
A1  - Tarkhanov, Nikolai Nikolaevich
T1  - On completeness of root functions of Sturm-Liouville problems with discontinuous boundary operators
N2  - 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.
T3  - Preprints des Instituts für Mathematik der Universität Potsdam - 1(2012)11 
KW  - Sturm-Liouville problems
KW  - discontinuous Robin condition
KW  - root functions
KW  - Lipschitz domains
Y1  - 2012
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-57759
SN  - 2193-6943
ER  -