TY  - INPR
A1  - Xiaochun, Liu
A1  - Witt, Ingo
T1  - Pseudodifferential calculi on the half-line respecting prescribed asymptotic types
N2  - Contents: 1. Introduction 2. Preliminaries 3. Basic Elements of the Calculus 4. Further Elements of the Calculus
T3  - Preprint - (2002) 06 
Y1  - 2002
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26255
ER  - 
TY  - INPR
A1  - Xiaochun, Liu
A1  - Schulze, Bert-Wolfgang
T1  - Boundary value problems in edge representation
N2  - Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.
T3  - Preprint - (2004) 14 
KW  - Boundary value problems
KW  - edge singularities
KW  - ellipticity in the edge calculus
Y1  - 2004
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-26746
ER  - 
TY  - INPR
A1  - Xiaochun, Liu
A1  - Witt, Ingo
T1  - Asymptotic expansions for bounded solutions to semilinear Fuchsian equations
N2  - It is shown that bounded solutions to semilinear elliptic Fuchsian equations obey complete asymptoic expansions in terms of powers and logarithms in the distance to the boundary. For that purpose, Schuze's notion of asymptotic type for conormal asymptotics close to a conical point is refined. This in turn allows to perform explicit calculations on asymptotic types - modulo the resolution of the spectral problem for determining the singular exponents in the asmptotic expansions.
T3  - Preprint - (2001) 01 
KW  - Calculus of conormal symbols
KW  - conormal asymptotic expansions
KW  - discrete saymptotic types
KW  - weighted Sobolev spaces with discrete saymptotics
Y1  - 2001
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-25912
ER  -