Classical Solutions; the Schauder Approach

  • David Gilbarg
  • Neil S. Trudinger
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 224)


This chapter develops a theory of second order linear elliptic equations that is essentially an extension of potential theory. It is based on the fundamental observation that equations with Hölder continuous coefficients can be treated locally as a perturbation of constant coefficient equations. From this fact Schauder [SC 4, 5] was able to construct a global theory, an extension of which is presented here. Basic to this approach are apriori estimates of solutions, extending those of potential theory to equations with Hölder continuous coefficients.


Dirichlet Problem Classical Solution Interpolation Inequality Interior Estimate Local Barrier 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • David Gilbarg
    • 1
  • Neil S. Trudinger
    • 2
  1. 1.Department of MathematicsStanford UniversityStanfordUSA
  2. 2.Department of Pure MathematicsAustralian National UniversityCanberraAustralia

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