Boundary Value Problems with Global Projection Conditions

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 th...

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Main Authors: Liu, Xiaochun, Schulze, Bert-Wolfgang (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham Springer International Publishing 2018, 2018
Edition:1st ed. 2018
Series:Advances in Partial Differential Equations
Subjects:
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a Introduction -- Boundary Value Problems with Global Projection Conditions -- Edge Operators with Global Projection Conditions -- BVPs without the Transmission Property 
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653 |a Global Analysis and Analysis on Manifolds 
653 |a Operator Theory 
653 |a Partial Differential Equations 
653 |a Operator theory 
653 |a Global analysis 
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520 |a 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