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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