The Bi-Laplacian with Wentzell Boundary Conditions on Lipschitz Domains

We investigate the Bi-Laplacian with Wentzell boundary conditions in a bounded domain $\Omega\subseteq\mathbb{R}^d$ Lipschitz $\Gamma$. More precisely, using form methods, we show that associated operator on ground space $L^2(\Omega)\times L^2(\Gamma)$ has compact resolvent and generates holomorphic strongly continuous real semigroup of self-adjoint operators. Furthermore, give full characterization terms Sobolev spaces, also proving H\"older regularity solutions, allowing classical interpretation condition. Finally, spectrum asymptotic behavior semigroup, as well eventual positivity.