论文标题
在二阶椭圆算子的数值范围内，$ l^p $中的混合边界条件
On the numerical range of second order elliptic operators with mixed boundary conditions in $L^p$
论文作者
论文摘要
我们考虑具有实际非对称系数函数的二阶椭圆运算符，该功能受到混合边界条件的影响。本文的目的是以最直接的方式对这些运营商在$ l^p $上实现的统一解析估计，并在最小的规律性假设上对域上的实现。这类似于[Chill等人的主要结果。 2006]。还考虑了相关半群的超包性。所有结果均适用于两个不同的形式域，以实现混合边界条件。我们进一步考虑了罗宾（Robin）的情况 - 而不是经典的诺伊曼（Neumann） - 边界条件，还允许操作员诱导动态边界条件。结果与诱导混合边界条件的形式域的元素的固有表征相辅相成。
We consider second order elliptic operators with real, nonsymmetric coefficient functions which are subject to mixed boundary conditions. The aim of this paper is to provide uniform resolvent estimates for the realizations of these operators on $L^p$ in a most direct way and under minimal regularity assumptions on the domain. This is analogous to the main result in [Chill et al. 2006]. Ultracontractivity of the associated semigroups is also considered. All results are for two different form domains realizing mixed boundary conditions. We further consider the case of Robin -- instead of classical Neumann -- boundary conditions and also allow for operators inducing dynamic boundary conditions. The results are complemented by an intrinsic characterization of elements of the form domains inducing mixed boundary conditions.
