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Analysis on Manifolds with Singularities / Der-Chen Chang, Bert-Wolfgang Schulze

By: Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Pseudo-Differential Operators, Theory and Applications ; 16Publisher: Cham : Birkhäuser, 2025Description: 1 Online-Ressource(X, 135 p. 1 illus. in color.)ISBN:
  • 9783032018908
Subject(s): Additional physical formats: 9783032018892 | 9783032018915 | Erscheint auch als: 9783032018892 Druck-Ausgabe | Erscheint auch als: 9783032018915 Druck-Ausgabe | Erscheint auch als: Analysis on manifolds with singularities. Druck-Ausgabe Cham, Switzerland : Birkhäuser, 2025. x, 135 SeitenDDC classification:
  • 515 23
DOI: DOI: 10.1007/978-3-032-01890-8Online resources: Summary: 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.Summary: 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-differential structures and establishes new insight to building up singular operators in corresponding operator algebras with symbolic structures. Researchers in the field will find the presented techniques in this book a valuable resource and inspiration for their own projects.PPN: PPN: 1947810561Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SMA | ZDB-2-SXMS
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