论文标题
狮子的表示定理和应用
Lions' representation theorem and applications
论文作者
论文摘要
狮子的表示定理（RTL）是Lax--milgram定理的一个版本，其中一个空间的完整性未完成。在本文中，RTL是从规范空间上的操作器理论版本中推导的。本文的要点是基于RTL的推导理论，证明了该理论。一个应用程序涉及具有新的初始值和时间变量的周期性边界条件的非自主进化方程。
The Representation Theorem of Lions (RTL) is a version of the Lax--Milgram Theorem where completeness of one of the spaces is not complete. In this paper, RTL is deduced from an operator-theoretical version on normed space. The main point of the paper is a theory of derivations, based on RTL, for which well-posedness is proved. One application concerns non-autonomous evolution equations with a new initial-value and a periodic boundary condition for the time variable.
