TY  - INPR
A1  - Kapanadze, David
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential crack theory
N2  - Crack problems are regarded as elements in a pseudo-differential algbra, where the two sdes int S± of the crack S are treated as interior boundaries and the boundary Y of the crack as an edge singularity. We employ the pseudo-differential calculus of boundary value problems with the transmission property near int S± and the edge pseudo-differential calculus (in a variant with Douglis-Nirenberg orders) to construct parametrices od elliptic crack problems (with extra trace and potential conditions along Y) and to characterise asymptotics of solutions near Y (expressed in the framework of continuous asymptotics). Our operator algebra with boundary and edge symbols contains new weight and order conventions that are necessary also for the more general calculus on manifolds with boundary and edges.
T3  - Preprint - (2000) 09 
KW  - Crack theory
KW  - pseudo-differential boundary value problems
KW  - operator algebras on manifolds with singularities
KW  - conormal asymptotics
Y1  - 2000
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25759
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  -