标题： 一些奇异度量的Weyl公式及其在气态巨行星声学模态中的应用 显示英文标题

标题： Weyl formulae for some singular metrics with application to acoustic modes in gas giants

摘要： 本文的动机来自于对气态巨行星内部声波传播反问题的最新研究。 在这样的行星中，声速是各向同性的，并且在表面处趋于零。 从几何上看，这对应于一个带有边界的整体黎曼流形，其度量在边界附近发散。 在此，给出了相应拉普拉斯-贝尔特拉米算子的谱分析，并推导出了维伊尔定律。 所涉及的指数取决于豪斯多夫维数，在超临界情况下，该维数大于拓扑维数。 显示英文摘要

摘要： This paper is motivated by recent works on inverse problems for acoustic wave propagation in the interior of gas giant planets. In such planets, the speed of sound is isotropic and tends to zero at the surface. Geometrically, this corresponds to a Riemannian manifold with boundary whose metric blows up near the boundary. Here, the spectral analysis of the corresponding Laplace-Beltrami operator is presented and the Weyl law is derived. The involved exponents depend on the Hausdorff dimension which, in the supercritical case, is larger than the topological dimension.