Recent Progress on Boundary Blow-up

  • Satyanad Kichenassamy
Chapter
Part of the Progress in Nonlinear Differential Equations and Their Applications book series (PNLDE, volume 63)

Abstract

We report on the solution of two long-standing conjectures on the boundary behavior of maximal solutions of semilinear elliptic equations, focusing on the proof of the boundary regularity of the hyperbolic radius in higher dimensions. The main tool is the reduction of the problem to a degenerate equation of Fuchsian type, for which new Schauder-type estimates are proved. We also sketch an algorithm suitable for large classes of applications.

Keywords

Singular Solution Nonlinear Wave Equation Boundary Behavior Maximal Solution Nonlinear PDEs 
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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2005

Authors and Affiliations

  • Satyanad Kichenassamy
    • 1
  1. 1.Laboratoire de Mathématiques (UMR 6056)CNRS & Université de Reims Champagne-ArdenneReims Cedex 2France

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