Boundary-Value Problems for Laplace’s Equation. Theory of Linear Equations and Systems
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.
KeywordsDirichlet Problem Neumann Problem Principal Symbol Linear Partial Differential Equation Exterior Problem
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