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Boundary Value Problems with Global Projection Conditions - Xiaochun Liu, Bert-Wolfgang Schulze

Boundary Value Problems with Global Projection Conditions

Buch | Hardcover
XVI, 410 Seiten
2018 | 1st ed. 2018
Springer International Publishing (Verlag)
978-3-319-70113-4 (ISBN)
CHF 149,75 inkl. MwSt
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This book presents boundary value problems for arbitrary elliptic pseudo-differential operators on a smooth compact manifold with boundary. In this regard, every operator admits global projection boundary conditions, giving rise to analogues of Toeplitz operators in subspaces of Sobolev spaces on the boundary associated with pseudo-differential projections. The book describes how these operator classes form algebras, and establishes the concept for Boutet de Monvel's calculus, as well as for operators on manifolds with edges, including the case of operators without the transmission property. Further, it shows how the calculus contains parametrices of elliptic elements. Lastly, the book describes natural connections to ellipticity of Atiyah-Patodi-Singer type for Dirac and other geometric operators, in particular spectral boundary conditions with Calderón-Seeley projections and the characterization of Cauchy data spaces.


Introduction.- Boundary Value Problems with Global Projection Conditions.- Edge Operators with Global Projection Conditions.- BVPs without the Transmission Property.

"The book is very nice and carefully written, and is a very valuable contribution to the subject ... . It is well suited to experts but also to Ph.D. students who are willing to pursue this beautiful and rich area of research." (Alberto Parmeggiani, Mathematical Reviews, August, 2019)
"The present book is devoted to developing general concepts of ellipticity of boundary value problems (BVPs) and provides a self-contained resource for use by professional researchers." (David Kapanadze, zbMATH 1423.35003, 2019)

Erscheinungsdatum
Reihe/Serie Advances in Partial Differential Equations
Operator Theory: Advances and Applications
Zusatzinfo XVI, 410 p.
Verlagsort Cham
Sprache englisch
Maße 155 x 235 mm
Gewicht 759 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte elliptic operators • global projection conditions • Laplacian • Partial differential equations • pseudo-differential operators • Shapiro-Lopatinskij ellipticity
ISBN-10 3-319-70113-4 / 3319701134
ISBN-13 978-3-319-70113-4 / 9783319701134
Zustand Neuware
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