# Elliptic Mixed, Transmission and Singular Crack Problems

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*Gohar Harutyunyan; Bert-Wolfgang Schulze*

A publication of the European Mathematical Society

Mixed, transmission, or crack problems belong to the analysis of
boundary value problems on manifolds with singularities. The Zaremba problem
with a jump between Dirichlet and Neumann conditions along an interface on the
boundary is a classical example. The central theme of this book is to study
mixed problems in standard Sobolev spaces as well as in weighted edge spaces
where the interfaces are interpreted as edges. Parametrices and regularity of
solutions are obtained within a systematic calculus of boundary value problems
on manifolds with conical or edge singularities. This calculus allows
singularities on the interface and homotopies between mixed and crack
problems. Additional edge conditions are computed in terms of relative index
results. In a detailed final chapter, the intuitive ideas of the approach are
illustrated, and there is a discussion of future challenges. A special feature
of the text is the inclusion of many worked-out examples which help the reader
to appreciate the scope of the theory and to treat new cases of practical
interest.

This book is addressed to mathematicians and physicists interested in models
with singularities, associated boundary value problems, and their solvability
strategies based on pseudo-differential operators. The material is also useful
for students in higher semesters and young researchers, as well as for
experienced specialists working in analysis on manifolds with geometric
singularities, the applications of index theory and spectral theory, operator
algebras with symbolic structures, quantisation, and asymptotic analysis.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

#### Readership

Graduate students and research mathematicians interested in differential equations.