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Harutyunyan G., Schulze B.-W. Elliptic Mixed, Transmission and Singular Crack Problems

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Harutyunyan G., Schulze B.-W. Elliptic Mixed, Transmission and Singular Crack Problems
European Mathematical Society, 2008. — 778 p. — (EMS Tracts in Mathematics 04). — ISBN 978-3-03719-040-1.
Elliptic mixed, transmission, or crack problems belong to the analysis on manifolds with singularities, more precisely, to the calculus of boundary value problems, where the data or the coefficients have singularities. A classical example is the Zaremba problem for the Laplace equation with mixed Dirichlet and Neumann conditions. Mixed problems in general are characterised by boundary conditions that have a jump along an interface on the boundary. At the same time the configuration may have singularities, e.g., conical points or edges, and it is an interesting task of the mathematical analysis to establish the properties of solvability.
Contents
Introduction
Boundary value problems with mixed and interface data
Symbolic structures and associated operators
Boundary value problems with the transmission
Mixed problems in standard Sobolev spaces
Mixed problems in weighted edge spaces
Operators on manifolds with conical singularities and boundary
Operators on manifolds with edges and boundary
Corner operators and problems with singular interfaces
Operators in infinite cylinders and the relative index
Intuitive ideas of the calculus on singular manifolds
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