Laplace Equation on the Boundary Value Problems
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Date
2014-06-06
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Addis Ababa University
Abstract
In this project we present basic properties of Laplace’s equation on the
boundary value problems with the tight focus on mean value property. It is
shown that for the Neumann problem,
Δ = 0 on Ω × (0 , ∞)
= ( )
The boundary data can’t be prescribed at will. Indeed, it is required to satisfy
the compatibility condition,
( ) = 0
Regular conditions on the solution u of Δ = 0 are also shown.
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Keywords
Laplace Equation, Boundary, Value, Problems