Laplace Equation On The Boundary Value Problems

In this project we present basic properties of Laplace’s equation on thernboundary value problems with the tight focus on mean value property. It isrnshown that for the Neumann problem,rnΔ = 0 on Ω × (0 , ∞)rn= ( )rnThe boundary data can’t be prescribed at will. Indeed, it is required to satisfyrnthe compatibility condition,rn( ) = 0rnRegular conditions on the solution u of Δ = 0 are also shown.

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