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Hadamard asymptotics for eigenvalues of the Dirichlet Laplacian
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2020-06-23 , DOI: 10.1016/j.matpur.2020.06.002 Vladimir Kozlov , Johan Thim
中文翻译:
Dirichlet Laplacian特征值的Hadamard渐近性
更新日期:2020-06-23
Journal de Mathématiques Pures et Appliquées ( IF 2.1 ) Pub Date : 2020-06-23 , DOI: 10.1016/j.matpur.2020.06.002 Vladimir Kozlov , Johan Thim
This paper is dedicated to the classical Hadamard formula for asymptotics of eigenvalues of the Dirichlet-Laplacian under perturbations of the boundary. We prove that the Hadamard formula still holds for -domains with -perturbations. We also derive an optimal estimate for the remainder term in the -case. Furthermore, if the boundary is merely Lipschitz, we show that the Hadamard formula is not valid.
中文翻译:
Dirichlet Laplacian特征值的Hadamard渐近性
本文致力于边界扰动下Dirichlet-Laplacian特征值渐近性的经典Hadamard公式。我们证明哈达玛公式仍然适用于-个域 -摄动。我们还得出了剩余项中的最优估计-案件。此外,如果边界仅是Lipschitz,则表明Hadamard公式无效。