Buchumschlag

Analysis on Manifolds with Singularities

This exposition introduces new developments of pseudo‐differential operators on manifolds with singularities such as conical points, edges, or higher corners, and recent results in these fields. It presents some crucial parts of recent inventions in singular analysis which contribute to pseudo-diffe...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Hauptverfasser: Chang, Der-Chen (VerfasserIn), Schulze, Bert-Wolfgang (VerfasserIn)
Körperschaft: SpringerLink (Online service)
Format: Elektronisch E-Book
Sprache:Englisch
Veröffentlicht: Cham : Springer Nature Switzerland : Imprint: Birkhäuser, 2025.
Ausgabe:1st ed. 2025.
Schriftenreihe:Pseudo-Differential Operators, Theory and Applications, 16
Schlagworte:
Mathematical analysis.
Operator theory.
Functional analysis.
Analysis.
Operator Theory.
Functional Analysis.
Online-Zugang:https://doi.org/10.1007/978-3-032-01890-8
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Inhaltsangabe:
  • Introduction
  • 1. Pseudo-differential operators - basics and new techniques
  • 1.1. Elements of the local calculus
  • 1.2. Operators on manifolds
  • 1.3. Twisted symbolic estimates
  • 1.4. Edge Sobolev spaces
  • 1.5. Explicit solutions to Dirichlet and Neumann problems
  • 1.6. Hölder and Lp estimates for coercive boundary value problems
  • 2. Operators of Fuchs Type
  • 2.1. Degenerate Operators and Singular Manifolds
  • 2.2. Kernel Cut-Off
  • 2.3. Symbols with Distributional Asymptotic Densities
  • 2.4. Conical singularities in stretched descripion
  • 2.5. The cone calculus
  • 3. Manifolds with edges
  • 3.1. Manifolds with edge and weighted Sobolev spaces
  • 3.2. Edge spaces with asymptotics
  • 3.3. Edge operators
  • 4. Edge Operators with Trace and Potential Conditions
  • 4.1. Basic Tools
  • 4.2. Group Actions and Weighted Cone and Edge Spaces
  • 4.3. Operators in Edge Spaces
  • 4.4. Notes on Pseudo-Differential Boundary Problems
  • 4.5. The Laplace-Beltrami Operator on a Wedge
  • 4.6. The Global Ellipticity of Edge Problems
  • 4.7. Local Calculus Close to the Edge
  • 4.8. Global Ellipticity with Edge Conditions
  • 5. The Geometry of Singularities
  • 5.1. The Case of Conical Singularities or Edges
  • 5.2. Higher Singularities
  • 5.3. Iterated Edge Spaces
  • 5.4. Distribution spaces and cone operators
  • Bibliography.

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