Hadamard variation of eigenvalues with respect to general domain perturbations
Spectral Theory
2024-06-06 v2 Analysis of PDEs
Abstract
We study Hadamard variation of eigenvalues of Laplacian with respect to general domain perturbations. We show their existence up to the second order rigorously and characterize the derivatives, using associated eigenvalue problems in finite dimensional spaces. Then smooth rearrangement of multiple eigenvalues is explicitly given. This result follows from an abstract theory, applicable to general perturbations of symmetric bilinear forms.
Keywords
Cite
@article{arxiv.2309.00273,
title = {Hadamard variation of eigenvalues with respect to general domain perturbations},
author = {Takashi Suzuki and Takuya Tsuchiya},
journal= {arXiv preprint arXiv:2309.00273},
year = {2024}
}
Comments
to appear in Journal of the Mathematical Society of Japan