Generalized Solutions and Regularity

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


This chapter treats linear elliptic operators having principal part in divergence form under relatively weak smoothness assumptions on the coefficients. We consider operators L of the form
$$ Lu = D_i \left( {a^{ij} \left( x \right)D_j u + b^i \left( x \right)u} \right) + c^i \left( x \right)D_i u + d\left( x \right)u $$
whose coefficients a ij , b i , c i , d (i, j = l, …, n) are assumed to be measurable functions on a domain Ω ⊂ ℝ n .


Generalize Solution Weak Solution Dirichlet Problem Harnack Inequality Strong Maximum Principle 
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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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