Fuchsian Reduction

This four-part text beautifully interweaves theory and applications in Fuchsian reduction. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses or as a resource for researchers.

This four-part text beautifully interweaves theory and applications in Fuchsian Reduction. Background results in weighted Sobolev and Holder spaces as well as Nash-Moser implicit function theorem are provided. Most chapters contain a problem section and notes with references to the literature. This volume can be used as a text in graduate courses in PDEs and/or Algebra, or as a resource for researchers working with applications to Fuchsian Reduction. The comprehensive approach features the inclusion of problems and bibliographic notes.

Fuchsian Reduction. - Formal Series. - General Reduction Methods. - Theory of Fuchsian Partial Di? erential Equations. - Convergent Series Solutions of Fuchsian Initial-Value Problems. - Fuchsian Initial-Value Problems in Sobolev Spaces. - Solution of Fuchsian Elliptic Boundary-Value Problems. - Applications. - Applications in Astronomy. - Applications in General Relativity. - Applications in Differential Geometry. - Applications to Nonlinear Waves. - Boundary Blowup for Nonlinear Elliptic Equations. - Background Results. - Distance Function and Hölder Spaces. - Nash Moser Inverse Function Theorem.