Maximum and Comparison Principles

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


The purpose of this chapter is to provide various maximum and comparison principles for quasilinear equations which extend corresponding results in Chapter 3. We consider second order, quasilinear operators Q of the form
$$Qu = a{i^j}\left( {x,u,Du} \right){D_{ij}}u + b\left( {x,u,Du} \right),\quad {a^{ij}} = {a^{ji}},$$


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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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