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Poisson’s Equation and the Newtonian Potential

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

Abstract

In Chapter 2 we introduced the fundamental solution Γ of Laplace’s equation given by
$$\Gamma \left( {x - y} \right) = \Gamma \left( {\left| {x - y} \right|} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{{n\left( {2 - n} \right){{\omega }_{n}}}}{{{\left| {x - y} \right|}}^{{2 - n}}},\,\quad n > 2} \\ {\frac{1}{{2\pi }}\log \left| {x - y} \right|,\quad \quad \quad \quad n = 2.} \\ \end{array} } \right.$$
(4.1)

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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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