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The Double-Layer Potential

  • Vladimir I. Arnold
Part of the Universitext book series (UTX)

Abstract

We have thus found the fundamental solution for the Laplacian in ℝ n :for n>2,
$$ {u_0} = \frac{1}{{ - \left( {n - 2} \right){\omega _{n - 1}}{r^{n - 2}}}} $$
, where ωn-1 is the surface of the unit ) sphere in ℝ n ; for n = 2,
$$ {u_0} = \frac{1}{{2\pi }}\ln \frac{1}{r}; $$
for n=1,
$$ {u_0} = \frac{{\left| x \right|}}{2} $$
.

Keywords

Unit Sphere Fundamental Solution Homogeneous Function Equipotential Surface Dipole Potential 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Vladimir I. Arnold
    • 1
    • 2
  1. 1.Steklov Mathematical InstituteMoscowRussia
  2. 2.CEREMADEUniversité de Paris-DauphineParis Cedex 16France

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