Equations in Two Variables

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


The theory of quasilinear elliptic equations in two dimensions is in many respects simpler and in some respects more general than that in higher dimensions. This chapter is concerned with aspects of the theory that are specifically two-dimensional in character, although the basic results on quasilinear equations can be extended to higher dimensions by other methods. As will be seen, the special features of this theory are founded on strong apriori estimates that are valid for general linear equations in two variables.


Elliptic Equation Dirichlet Problem Quasiconformal Mapping Quasilinear Elliptic Equation Slope Condition 
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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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