近超球面域的斯特克洛夫特征值

IF 2.9 3区 综合性期刊 Q1 MULTIDISCIPLINARY SCIENCES Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences Pub Date : 2024-04-03 DOI:10.1098/rspa.2023.0734
Chee Han Tan, Robert Viator
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引用次数: 0

摘要

我们考虑的是 Rd+1 中 d≥3 的近超球面域的 Steklov 特征值。在以前的工作中,我们将此类域视为球的扰动,证明了斯特克洛夫特征值是域扰动参数的解析函数。在这里,我们计算了渐近展开的一阶项,并证明一阶扰动是一个赫米矩阵的特征值,其项可以用波哈默和维格纳 3j 符号明确写出。我们对渐近展开进行了分析,并展示了具有固定体积的域之间的以下等周结果:(i) 对于斯特克洛夫特征值的一个无限子集,球不是最优的;(ii) 对于斯特克洛夫特征值的另一个无限子集,球是一个静止点。
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Steklov eigenvalues of nearly hyperspherical domains

We consider Steklov eigenvalues of nearly hyperspherical domains in Rd+1 with d3. In previous work, treating such domains as perturbations of the ball, we proved that the Steklov eigenvalues are analytic functions of the domain perturbation parameter. Here, we compute the first-order term of the asymptotic expansion and show that the first-order perturbations are eigenvalues of a Hermitian matrix, whose entries can be written explicitly in terms of Pochhammer’s and Wigner 3j-symbols. We analyse the asymptotic expansion and show the following isoperimetric results among domains with fixed volume: (i) for an infinite subset of Steklov eigenvalues, the ball is not optimal and (ii) for a different infinite subset of Steklov eigenvalues, the ball is a stationary point.

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来源期刊
CiteScore
6.40
自引率
5.70%
发文量
227
审稿时长
3.0 months
期刊介绍: Proceedings A has an illustrious history of publishing pioneering and influential research articles across the entire range of the physical and mathematical sciences. These have included Maxwell"s electromagnetic theory, the Braggs" first account of X-ray crystallography, Dirac"s relativistic theory of the electron, and Watson and Crick"s detailed description of the structure of DNA.
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