Topological Fixed Point Theorems and Their Application

  • David Gilbarg
  • Neil S. Trudinger
Part of the Classics in Mathematics book series (volume 224)


In this chapter the solvability of the classical Dirichlet problem for quasilinear equations is reduced to the establishment of certain apriori estimates for solutions. This reduction is achieved through the application of topological fixed point theorems in appropriate function spaces. We shall first formulate a general criterion for solvability and illustrate its application in a situation where the required apriori estimates are readily derived from our previous results. The derivation of these apriori estimates under more general hypotheses will be the major concern of the ensuing chapters.


Banach Space Weak Solution Point Theorem Dirichlet Problem Quasilinear Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • David Gilbarg
    • 1
  • Neil S. Trudinger
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.School of Mathematical SciencesThe Australian National UniversityCanberraAustralia

Personalised recommendations