I want to know the bi-Laplace equation with this two boundary conditions admits an unique solution in H2(Ω)H^2(\Omega), for given h∈H−1/2(∂Ω)h\in H^{-1/2}(\partial \Omega).

Δ2u=0,onΩ,\Delta ^2 u=0,\quad on\quad \Omega,

∂n(Δu)|∂Ω=0,Δu|∂Ω=h,\partial_n (\Delta u)\Big|_{\partial \Omega}=0,\qquad \Delta u\Big|_{\partial \Omega}=h,

where ∂n\partial_n denotes the normal derivative, nn is the outward unit normal to ∂Ω\partial \Omega.

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How do you understand these boundary conditions? Did you tried to write down a weak formulation (via integration by parts)?

– gerw

2 days ago

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