论文标题
Lipschitz域上具有Wentzell边界条件的Bi-Laplacian
The Bi-Laplacian with Wentzell boundary conditions on Lipschitz domains
论文作者
论文摘要
我们研究了带有有限域$ω\ subseteq \ mathbb {r}^d $带有Lipschitz边界$γ$的BI-LAPLACIAN具有Wentzell边界条件的Bi-Laplacian。更确切地说，使用形式方法，我们表明，地面空间上的相关运算符$ l^2（ω）\ times l^2（γ）$具有紧凑的分辨率，并产生了一个全体形态且强烈连续的自动化合物操作员的真实半群。此外，我们在Sobolev空间方面给出了域的全面表征，还证明了解决方案的规律性，从而可以对边界条件进行经典的解释。最后，我们研究了半群的光谱和渐近行为，以及最终的阳性。
We investigate the Bi-Laplacian with Wentzell boundary conditions in a bounded domain $Ω\subseteq\mathbb{R}^d$ with Lipschitz boundary $Γ$. More precisely, using form methods, we show that the associated operator on the ground space $L^2(Ω)\times L^2(Γ)$ has compact resolvent and generates a holomorphic and strongly continuous real semigroup of self-adjoint operators. Furthermore, we give a full characterization of the domain in terms of Sobolev spaces, also proving Hölder regularity of solutions, allowing classical interpretation of the boundary condition. Finally, we investigate spectrum and asymptotic behavior of the semigroup, as well as eventual positivity.
