论文标题
热弹性操作员痕迹的渐近膨胀
Asymptotic Expansions of The Traces of the Thermoelastic Operators
论文作者
论文摘要
我们在利马尼亚歧管上获得了热弹性操作员的痕迹的渐近膨胀，并提供了一种有效的方法来计算渐近扩张的所有系数。这些系数提供精确的几何信息。特别是，我们明确计算有关歧管及其边界体积的前两个系数。作为一种应用，通过将我们的结果与等仪不等式相结合，我们表明，在所有有界热弹性物体之间，其热弹性光谱在具有边界的所有有界热弹性物体中，其热弹性光谱是唯一确定的。
We obtain the asymptotic expansions of the traces of the thermoelastic operators with the Dirichlet and Neumann boundary conditions on a Riemannian manifold, and give an effective method to calculate all the coefficients of the asymptotic expansions. These coefficients provide precise geometric information. In particular, we explicitly calculate the first two coefficients concerning the volumes of the manifold and its boundary. As an application, by combining our results with the isoperimetric inequality we show that an $n$-dimensional geodesic ball is uniquely determined up to isometry by its thermoelastic spectrum among all bounded thermoelastic bodies with boundary.
