TY  - JOUR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary-contact problems for domains with conical singularities
N2  - We study boundary-contact problems for elliptic equations (and systems) with interfaces that have conical singularities. Such problems represent continuous operators between weighted Sobolev spaces and subspaces with asymptotics. Ellipticity is formulated in terms of extra transmission conditions along the interfaces with a control of the conormal symbolic structure near conical singularities. We show regularity and asymptotics of solutions in weighted spaces, and we construct parametrices. The result will be illustrated by a number of explicit examples. (c) 2004 Elsevier Inc. All rights reserved
Y1  - 2005
SN  - 0022-0396
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary-contact Problems for Domains with Conical Singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2004
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary-contact Problems for Domains with Edges Singularities
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2005
SN  - 1613-3307
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotics of potentials in the edge calculus
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2003
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems on manifolds with exits to infinity
N2  - We construct a new calculus of boundary value problems with the transmission property on a non-compact smooth manifold with boundary and conical exits to infinity. The symbols are classical both in covariables and variables. The operators are determined by principal symbol tuples modulo operators of lower orders and weights (such remainders are compact in weighted Sobolev spaces). We develop the concept of ellipticity, construct parametrices within the algebra and obtain the Fredholm property. For the existence of Shapiro-Lopatinskij elliptic boundary conditions to a given elliptic operator we prove an analogue of the Atiyah-Bott condition.
T3  - Preprint - (2000) 06 
KW  - pseudo-differentialboundary value problems
KW  - elliptic operators on non-compact manifolds
KW  - Atiyah-Bott condition
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25727
ER  - 
TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic calculus for boundary value problems on manifolds with edges
N2  - Boundary value problems for (pseudo-) differential operators on a manifold with edges can be characterised by a hierarchy of symbols. The symbol structure is responsible or ellipicity and for the nature of parametrices within an algebra of "edge-degenerate" pseudo-differential operators. The edge symbol component of that hierarchy takes values in boundary value problems on an infinite model cone, with edge variables and covariables as parameters. Edge symbols play a crucial role in this theory, in particular, the contribution with holomorphic operatot-valued Mellin symbols. We establish a calculus in s framework of "twisted homogenity" that refers to strongly continuous groups of isomorphisms on weighted cone Sobolev spaces. We then derive an equivalent representation with a particularly transparent composition behaviour.
T3  - Preprint - (2001) 21 
KW  - pseudo-differential boundary value problems
KW  - operators on manifolds with singularities
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26046
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Crack theory and edge singularities
T3  - Mathematics and its applications
Y1  - 2003
SN  - 1-4020-1524-0
VL  - 561
PB  - Kluwer Acad. Publ
CY  - Dordrecht
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Symbolic calcullus for boundary value problems on manifolds with edges
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe Partiell
Y1  - 2001
SN  - 1437-739X
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Crack theory and edge singularities : Chapter III
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe partiell
Y1  - 2001
SN  - 1437-739x
PB  - Univ.
CY  - Potsdam
ER  - 
TY  - BOOK
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Crack theory and edge singularities : Chapter V
T3  - Preprint / Universität Potsdam, Institut für Mathematik, Arbeitsgruppe partiell
Y1  - 2001
SN  - 1437-739x
PB  - Univ.
CY  - Potsdam
ER  -