$\int_{\partial \Omega}(-v\nabla \Delta u\cdot\mathbf{n}+\alpha\nabla^{T}vH_{u} \mathbf{n})ds=0$, for all $v$ which satisfies$\nabla v\cdot n =0$ on $\partial \Omega$, derive the boundary condition:$\nabla \Delta u\cdot\mathbf{n}+\alpha \nabla(\mathbf{t}^{T}H_{u}\mathbf{n})\cdot \mathbf{t}=0$ on $\partial \Omega$. $\mathbf{n}$ is unit normal and $\mathbf{t}$ is unit tangent vector along the boundary.

I have no idea how to get this boundary condition.


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