By Gohar Harutyunyan

Combined, transmission, or crack difficulties belong to the research of boundary worth difficulties on manifolds with singularities. The Zaremba challenge with a bounce among Dirichlet and Neumann stipulations alongside an interface at the boundary is a classical instance. The critical topic of this ebook is to review combined difficulties in regular Sobolev areas in addition to in weighted aspect areas the place the interfaces are interpreted as edges. Parametrices and regularity of ideas are acquired inside a scientific calculus of boundary worth difficulties on manifolds with conical or facet singularities. This calculus permits singularities at the interface and homotopies among combined and crack difficulties. extra side stipulations are computed when it comes to relative index effects. In a close ultimate bankruptcy, the intuitive rules of the method are illustrated, and there's a dialogue of destiny demanding situations. a distinct characteristic of the textual content is the inclusion of many worked-out examples which support the reader to understand the scope of the idea and to regard new situations of sensible curiosity. This booklet is addressed to mathematicians and physicists drawn to types with singularities, linked boundary price difficulties, and their solvability concepts in line with pseudo-differential operators. the cloth is additionally invaluable for college kids in better semesters and younger researchers, in addition to for skilled experts operating in research on manifolds with geometric singularities, the purposes of index conception and spectral conception, operator algebras with symbolic buildings, quantisation, and asymptotic research. A booklet of the ecu Mathematical Society (EMS). dispensed in the Americas by means of the yankee Mathematical Society.