Analysis on Manifolds with Singularities

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.