TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Pseudo-differential calculus on manifolds with geometric singularities
N2  - Differential and pseudo-differential operators on a manifold with (regular) geometric singularities can be studied within a calculus, inspired by the concept of classical pseudo-differential operators on a C1 manifold. In the singular case the operators form an algebra with a principal symbolic hierarchy σ = (σj)0≤j≤k, with k being the order of the singularity and σk operator-valued for k ≥ 1. The symbols determine ellipticity and the nature of parametrices. It is typical in this theory that, similarly as in boundary value problems (which are special edge problems, where the edge is just the boundary), there are trace, potential and Green operators, associated with the various strata of the configuration. The operators, obtained from the symbols by various quantisations, act in weighted distribution spaces with multiple weights. We outline some essential elements of this calculus, give examples and also comment on new challenges and interesting problems of the recent development.
T3  - Preprint - (2006) 20 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30204
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - Elliptic differential operators on manifolds with edges
N2  - On a manifold with edge we construct a specific class of (edgedegenerate) elliptic differential operators. The ellipticity refers to the principal symbolic structure σ = (σψ, σ^) of the edge calculus consisting of the interior and edge symbol, denoted by σψ and σ^, respectively. For our choice of weights the ellipticity will not require additional edge conditions of trace or potential type, and the operators will induce isomorphisms between the respective edge spaces.
T3  - Preprint - (2006) 18 
KW  - Operators on manifolds with edge
KW  - ellipticity with respect to interior and edge symbols
KW  - weighted edge spaces
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30188
ER  - 
TY  - INPR
A1  - Schulze, Bert-Wolfgang
T1  - The structure of operators on manifolds with polyhedral singularities
N2  - We discuss intuitive ideas and historical background of concepts in the analysis on configurations with singularities, here in connection with our iterative approach for higher singularities.
T3  - Preprint - (2006) 05 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30099
ER  - 
TY  - INPR
A1  - Kapanadze, D.
A1  - Schulze, Bert-Wolfgang
A1  - Seiler, J.
T1  - Operators with singular trace conditions on a manifold with edges
N2  - We establish a new calculus of pseudodifferential operators on a manifold with smooth edges and study ellipticity with extra trace and potential conditions (as well as Green operators) at the edge. In contrast to the known scenario with conditions of that kind in integral form we admit in this paper ‘singular’ trace, potential and Green operators, which are related to the corresponding operators of positive type in Boutet de Monvel’s calculus for boundary value problems.
T3  - Preprint - (2006) 01 
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30058
ER  - 
TY  - INPR
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems in weighted edge spaces
N2  - We study elliptic boundary value problems in a wedge with additional edge conditions of trace and potential type. We compute the (difference of the) number of such conditions in terms of the Fredholm index of the principal edge symbol. The task will be reduced to the case of special opening angles, together with a homotopy argument.
T3  - Preprint - (2006) 09 
KW  - Elliptic operators in domains with edges
KW  - boundary value problems
KW  - weighted edge spaces
Y1  - 2006
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-30104
ER  -