论文标题
Wentzell Laplacian通过形式和近似迹线
The Wentzell Laplacian via forms and the approximative trace
论文作者
论文摘要
我们使用表单方法来定义与Wentzell边界条件的域$ω$上的laplacian的合适实现，即，$ \ partial _ {\ mathrm {n}} u +βU +βU +Δu= 0 $在适当的含义上保持在$ $ω$的边界上。为了实现这些实现，我们研究了它们的半群生成属性。使用近似迹线，我们提供了一种统一的处理，该处理部分允许不规则甚至分形域。此外，我们承认$β$基本上是有界和复杂值的。如果域是Lipschitz，我们将获得一个内核连续到边界。
We use form methods to define suitable realisations of the Laplacian on a domain $Ω$ with Wentzell boundary conditions, i.e. such that $\partial_{\mathrm{n}}u + βu + Δu = 0$ holds in a suitable sense on the boundary of $Ω$. For those realisations, we study their semigroup generation properties. Using the approximative trace, we give a unified treatment that in part allows irregular and even fractal domains. Moreover, we admit $β$ to be merely essentially bounded and complex-valued. If the domain is Lipschitz, we obtain a kernel continuous up to the boundary.
