∫∂Ω∂u[∂N}dσ if Δu=0 in Ω?Is it always possible to solve an equation u″=0 in [0,1]...

Patricia Crane

Patricia Crane



Ωu[N}dσ if Δu=0 in Ω?
Is it always possible to solve an equation u=0 in [0,1] if u(0) and u(1) are given?(What is connection to first question?) Is the solution - unique?

Answer & Explanation

Neil Dismukes

Neil Dismukes


2022-01-19Added 37 answers

For the first one
From the divergence theorem for the vector field gradu we get that:
Ω÷( u)ν=Ω<u,N>σ
where ν is the volume element.
Using now the ypothesis that 0=Δu=÷( u) and that uN=< g,N>

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