Boundary Value Problems with Global Projection Conditions

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Synopsis

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.

Book details

Author:
Xiaochun Liu, Bert-Wolfgang Schulze
ISBN:
9783319701141
Related ISBNs:
9783319701134
Publisher:
Springer International Publishing
Pages:
N/A
Reading age:
Not specified
Includes images:
No
Date of addition:
2018-11-04
Usage restrictions:
Copyright
Copyright date:
2018
Copyright by:
N/A 
Adult content:
No
Language:
English
Categories:
Mathematics and Statistics, Nonfiction