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I'm looking for a reference showing how to obtain a priori estimate for solutions to a linear second-order elliptic equation with Wentzell boundary condition in a bounded domain in $H^1$ space.

The problem I'm considering is \begin{equation}\begin{cases} Lu = \partial_i(a^{ij}\partial_j u) + b^i\partial_i u + cu & = & f &\mbox{in } \Omega \\ Bu = \alpha^{st}D_{st}u + \beta^sD_su+\gamma u & = & g &\mbox{on } \partial\Omega \end{cases}\end{equation}

Thank you.

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  • $\begingroup$ Maybe this kind of equation should refer the relavence paper. $\endgroup$
    – monotone operator
    Commented Dec 13, 2023 at 5:08

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