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

Manifold Enea 

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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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