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. (C R Acad Sci Paris 342:909–914, 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 characterisation of elements of the form domains inducing mixed boundary conditions.

我们考虑具有实数，非对称系数函数的二阶椭圆算子，这些函数受混合边界条件的影响。本文的目的是为\（L ^ p \）上这些算子的实现提供统一的分解估计。以最直接的方式并在最小规则性假设下对该域进行操作。这类似于Chill等人的主要结果。（CR Acad Sci Paris 342：909-914，2006年）。还考虑了相关半群的超收缩性。所有结果均针对实现混合边界条件的两个不同形式域。我们进一步考虑Robin的情况，而不是经典的Neumann边界条件，并且还允许算符推导动态边界条件。结果由诱导混合边界条件的形式域元素的固有表征得到补充。