The Classical Maximum Principle

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


The purpose of this chapter is to extend the classical maximum principles for the Laplace operator, derived in Chapter 2, to linear elliptic differential operators of the form
$$ Lu = {a^{{ij}}}(x){D_{{ij}}}u + {b^i}(x){D_i}u + c(x)u, {a^{{ij = }}}{a^{{ji}}} $$
, where x = (x1,..., xn) lies in a domain Ω of ℝ n , n≥2. It will be assumed, unless otherwise stated, that u belongs to C2(Ω). The summation convention that repeated indices indicate summation from 1 to n is followed here as it will be throughout. L will always denote the operator (3.1).


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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

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