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.
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© 2004 Springer-Verlag Berlin Heidelberg
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Arnold, V.I. (2004). Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems. In: Lectures on Partial Differential Equations. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05441-3_12
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DOI: https://doi.org/10.1007/978-3-662-05441-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-40448-4
Online ISBN: 978-3-662-05441-3
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