LEADER 02943nam 22003975a 450 001 9910151935903321 005 20091109150325.0 010 $a3-03719-540-1 024 70$a10.4171/040 035 $a(CKB)3710000000953816 035 $a(CH-001817-3)64-091109 035 $a(PPN)178155306 035 $a(EXLCZ)993710000000953816 100 $a20091109j20071121 fy 0 101 0 $aeng 135 $aurnn|mmmmamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aElliptic Mixed, Transmission and Singular Crack Problems$b[electronic resource] /$fGohar Harutyunyan, B.-Wolfgang Schulze 210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2007 215 $a1 online resource (777 pages) 225 0 $aEMS Tracts in Mathematics (ETM)$v4 330 $aMixed, 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. 606 $aDifferential equations$2bicssc 606 $aPartial differential equations$2msc 615 07$aDifferential equations 615 07$aPartial differential equations 686 $a35-xx$2msc 700 $aHarutyunyan$b Gohar$0471670 702 $aSchulze$b B.-Wolfgang 801 0$bch0018173 906 $aBOOK 912 $a9910151935903321 996 $aElliptic Mixed, Transmission and Singular Crack Problems$92565751 997 $aUNINA