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  - Jaiani, George
A1  - Schulze, Bert-Wolfgang
T1  - Some degenerate elliptic systems and applications to cusped plates
N2  - The tension-compression vibration of an elastic cusped plate is studied under all the reasonable boundary conditions at the cusped edge, while at the noncusped edge displacements and at the upper and lower faces of the plate stresses are given.
T3  - Preprint - (2004) 27 
KW  - Casped plates
KW  - vibration
KW  - degenerate elliptic systems
KW  - weighted spaces
KW  - Hardy‘s inequality
KW  - Korn’s weighted inequality
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26866
ER  -