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

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

Abstract

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.

Keywords

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