Fuchsian reduction : applications to geometry, cosmology and mathematical physics

Includes bibliographical references (p. [277]-285) and index.

1. Introduction -- Pt. I. Fuchsian Reduction -- 2. Formal Series -- 3. General Reduction Methods -- Pt. II. Theory of Fuchsian Partial Differential Equations -- 4. Convergent Series Solutions of Fuchsian Initial-Value Problems -- 5. Fuchsian Initial-Value Problems in Sobolev Spaces -- 6. Solution of Fuchsian Elliptic Boundary-Value Problems -- Pt. III. Applications -- 7. Applications in Astronomy -- 8. Applications in General Relativity -- 9. Applications in Differential Geometry -- 10. Applications to Nonlinear Waves -- 11. Boundary Blowup for Nonlinear Elliptic Equations -- Pt. IV. Background Results -- 12. Distance Function and Holder Spaces -- 13. Nash-Moser Inverse Function Theorem.

"This work unfolds systematically in four parts, interweaving theory and applications. The case studies examined in Part III illustrate the impact of reduction techniques, and may serve as prototypes for future new applications. In the same spirit most chapters include a problem section. Background results and solutions to selected problems close the volume." "This book can be used as a text in graduate courses in pure or applied analysis, or as a resource for researchers working with singularities in geometry and mathematical physics."--BOOK JACKET.