论文标题
Banach空间中的最大$ l^p $ regularity的Staffans-Weiss扰动
Staffans-Weiss perturbations for Maximal $L^p$-regularity in Banach spaces
论文作者
论文摘要
在本文中，我们表明，在一大批无限制的扰动下，即Staffans-Weiss扰动，最大$ l^p $ regularity的概念是稳定的。为此，我们首先证明，在这类扰动下保留了半群的分析性，这是最大规律性的必要条件。在UMD空间中，利用$ \ Mathcal {r} $ - 有限条件来保证条件保证最大规律性。对于非反射性Banach空间，与边界值问题相关的Dirichlet操作员施加了条件，以证明最大规律性。提出了一个示例理论和应用于一类非自治的边界价值问题的PDE示例。
In this paper we show that the concept of maximal $L^p$-regularity is stable under a large class of unbounded perturbations, namely Staffans-Weiss perturbations. To that purpose, we first prove that the analyticity of semigroups is preserved under this class of perturbations, which is a necessary condition for the maximal regularity. In UMD spaces, $\mathcal{R}$-boundedness conditions are exploited to give conditions guaranteing the maximal regularity. For non-reflexive Banach space, a condition is imposed to the Dirichlet operator associated to the boundary value problem to prove the maximal regularity. A Pde example illustrating the theory and an application to a class of non-autonomous perturbed boundary value problems are presented.
