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Boundary Value Problems with Global Projection Conditions

  • Xiaochun Liu
  • Bert-Wolfgang Schulze

Part of the Operator Theory: Advances and Applications book series (OT, volume 265)

Also part of the Advances in Partial Differential Equations book sub series (APDE, volume 265)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Boundary Value Problems with Global Projection Conditions

    1. Front Matter
      Pages 1-1
    2. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 3-92
    3. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 93-144
    4. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 145-166
    5. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 167-178
    6. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 179-200
  3. Edge Operators with Global Projection Conditions

    1. Front Matter
      Pages 201-201
    2. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 203-284
    3. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 285-306
    4. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 307-320
    5. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 321-330
  4. BVPs without the Transmission Property

    1. Front Matter
      Pages 331-331
    2. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 333-348
    3. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 349-354
    4. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 355-360
    5. Xiaochun Liu, Bert-Wolfgang Schulze
      Pages 361-396
  5. Back Matter
    Pages 397-410

About this book

Introduction

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.

Keywords

partial differential equations Laplacian elliptic operators Pseudo-differential operators global projection conditions Shapiro-Lopatinskij ellipticity

Authors and affiliations

  • Xiaochun Liu
    • 1
  • Bert-Wolfgang Schulze
    • 2
  1. 1.School of Mathematics and StatisticsWuhan UniversityWuhanChina
  2. 2.Institut für MathematikUniversität Potsdam PotsdamGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-70114-1
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-70113-4
  • Online ISBN 978-3-319-70114-1
  • Series Print ISSN 0255-0156
  • Series Online ISSN 2296-4878
  • Buy this book on publisher's site
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