TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Calculus on a Manifold with Edge and Boundary
JF  - Complex analysis and operator theory
N2  - We study elements of the calculus of boundary value problems in a variant of Boutet de Monvel’s algebra (Acta Math 126:11–51, 1971) on a manifold N with edge and boundary. If the boundary is empty then the approach corresponds to Schulze (Symposium on partial differential equations (Holzhau, 1988), BSB Teubner, Leipzig, 1989) and other papers from the subsequent development. For non-trivial boundary we study Mellin-edge quantizations and compositions within the structure in terms a new Mellin-edge quantization, compared with a more traditional technique. Similar structures in the closed case have been studied in Gil et al.
KW  - algebra
KW  - Mellin quantization
Y1  - 2019
U6  - https://doi.org/10.1007/s11785-018-0800-y
SN  - 1661-8254
SN  - 1661-8262
VL  - 13
IS  - 6
SP  - 2627
EP  - 2670
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Khalil, Sara
A1  - Schulze, Bert-Wolfgang
T1  - Boundary problems on a manifold with edge
JF  - Asian-European Journal of Mathematics
N2  - We establish a calculus of boundary value problems (BVPs) on a manifold N with boundary and edge, based on Boutet de Monvel’s theory of BVPs in the case of a smooth boundary and on the edge calculus, where in the present case the model cone has a base which is a compact manifold with boundary. The corresponding calculus with boundary and edge is a unification of both structures and controls different operator-valued symbolic structures, in order to obtain ellipticity and parametrices.
KW  - manifolds with edge and boundary
KW  - distribution with asymptotics
KW  - ellipticity
KW  - Fredholm property
Y1  - 2017
U6  - https://doi.org/10.1142/S1793557117500875
SN  - 1793-5571
SN  - 1793-7183
VL  - 10
IS  - 2
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - THES
A1  - Khalil, Sara
T1  - Boundary Value Problems on Manifolds with Singularities
T1  - Randwertprobleme auf Mannigfaltigkeiten mit Singularitäten
N2  - In the thesis there are constructed new quantizations for pseudo-differential boundary value problems (BVPs) on manifolds with edge. The shape of operators comes from Boutet de Monvel’s calculus which exists on smooth manifolds with boundary. The singular case, here with edge and boundary, is much more complicated. The present approach simplifies the operator-valued symbolic structures by using suitable Mellin quantizations on infinite stretched model cones of wedges with boundary. The Mellin symbols themselves are, modulo smoothing ones, with asymptotics, holomorphic in the complex Mellin covariable. One of the main results is the construction of parametrices of elliptic elements in the corresponding operator algebra, including elliptic edge conditions.
N2  - In der Dissertation wurden neue Quantisierungen konstruiert für
pseudo-differentielle Randwertprobleme auf Mannigfaltigkeiten mit
Kanten-Singularitäten. Die Gestalt der hier behandelten Operatoren
ist motiviert durch Boutet de Monvels Kalkül, der auf glatten
Mannigfaltigkeiten mit Rand bekannt ist. Der singuläre Fall, hier mit
Kanten und Rand, ist weitaus komplizierter. Der gegenwärtige Zugang
vereinfacht die operatarwertigen Symbolstrukturen unter Verwendung
geeigneter Mellin-Quantisierungen auf unendlichen gestreckten Modell-
Kegeln, die entsprechenden Keilen mit Rand zugeordnet sind. Die
Mellin-Symbole selbst sind holomorph in der komplexen Mellin
Kovariablen bis auf glättende Restglieder mit Asymptotiken. Zu den
Hauptresultaten gehört die Konstruktion von Parametrices elliptischer
Elemente in der erzeugten Operator-Algebra, einschließlich
elliptischer Kanten-Bedingungen.
KW  - manifolds with singularities
KW  - boundary value problems
KW  - pseudo-differential equation
KW  - manifolds with edge
KW  - Boutet de Monvel's calculus
KW  - edge boundary value problems
KW  - Mannigfaltigkeiten mit Singularitäten
KW  - Randwertprobleme
KW  - pseudo-differentielle Gleichungen
KW  - Mannigfaltigkeiten mit Kante
KW  - Boutet de Monvels Kalkül
KW  - Kanten-Randwertprobleme
Y1  - 2018
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-419018
ER  -