Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems

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


Consider the compact connected smooth hypersurface Sn-1 in ℝn, which divides ℝn into two regions: the interior (bounded) region G and the exterior (unbounded) region G′. Suppose a continuous function f:S n-1→ℝ is given on the boundary. The Dirichlet problem for Laplace’s equation is to find a function u in the closure of the region G (G′) for which the following conditions hold.


Dirichlet Problem Neumann Problem Principal Symbol Linear Partial Differential Equation Exterior Problem 
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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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