TY  - JOUR
A1  - Chang, Der-Chen
A1  - Qian, Tao
A1  - Schulze, Bert-Wolfgang
T1  - Corner Boundary Value Problems
JF  - Complex analysis and operator theory
N2  - Boundary value problems on a manifold with smooth boundary are closely related to the edge calculus where the boundary plays the role of an edge. The problem of expressing parametrices of Shapiro-Lopatinskij elliptic boundary value problems for differential operators gives rise to pseudo-differential operators with the transmission property at the boundary. However, there are interesting pseudo-differential operators without the transmission property, for instance, the Dirichlet-to-Neumann operator. In this case the symbols become edge-degenerate under a suitable quantisation, cf. Chang et al. (J Pseudo-Differ Oper Appl 5(2014):69-155, 2014). If the boundary itself has singularities, e.g., conical points or edges, then the symbols are corner-degenerate. In the present paper we study elements of the corresponding corner pseudo-differential calculus.
KW  - Corner pseudo-differential operators
KW  - Ellipticity of corner-degenerate operators
KW  - Meromorphic operator-valued symbols
Y1  - 2015
U6  - https://doi.org/10.1007/s11785-014-0424-9
SN  - 1661-8254
SN  - 1661-8262
VL  - 9
IS  - 5
SP  - 1157
EP  - 1210
PB  - Springer
CY  - Basel
ER  - 
TY  - JOUR
A1  - Flad, H. -J.
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Asymptotic parametrices of elliptic edge operators
JF  - Journal of pseudo-differential operators and applications
N2  - We study operators on singular manifolds, here of conical or edge type, and develop a new general approach of representing asymptotics of solutions to elliptic equations close to the singularities. We introduce asymptotic parametrices, using tools from cone and edge pseudo-differential algebras. Our structures are motivated by models of many-particle physics with singular Coulomb potentials that contribute higher order singularities in Euclidean space, determined by the number of particles.
KW  - Cone and edge pseudo-differential operators
KW  - Ellipticity of edge-degenerate operators
KW  - Meromorphic operator-valued symbols
KW  - Asymptotics of solutions
Y1  - 2016
U6  - https://doi.org/10.1007/s11868-016-0159-7
SN  - 1662-9981
SN  - 1662-999X
VL  - 7
SP  - 321
EP  - 363
PB  - Springer
CY  - Basel
ER  -