Lamé算子泛函耗散性的判据
Criterion for the functional dissipativity of the Lamé operator
摘要：
在引入了定义域$Ω\subset {\mathbb R}^N$中狄利克雷问题的泛函耗散性的概念后，我们得到了二维Lamé系统泛函耗散性的充要条件，其中的偏微分算子系统的形式为$\partial_{h}({\mathscr A}^{hk}(x)\partial_{k})$（${\mathscr A}^{hk}(x)$是具有复值$L^\infty$元素的$m \times m$矩阵）.作为我们的理论的应用，我们提供了两个正则性结果的位移矢量在$N$维平衡问题，当身体是固定沿其边界。
英文摘要：
After introducing the concept of functional dissipativity of the Dirichlet problem in a domain $Ω\subset {\mathbb R}^N$ for systems of partial differential operators of the form $\partial_{h}({\mathscr A}^{hk}(x)\partial_{k})$ (${\mathscr A}^{hk}(x)$ being $m \times m$ matrices with complex valued $L^\infty$ entries), we find necessary and sufficient conditions for the functional dissipativity of the two-dimensional Lamé system. As an application of our theory we provide two regularity results for the displacement vector in the $N$-dimensional equilibrium problem, when the body is fixed along its boundary.
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