A shape variation result via the geometry of eigenfunctions
Analysis of PDEs
2021-07-21 v2 Optimization and Control
Abstract
We discuss some of the geometric properties, such as the foliated Schwarz symmetry, the monotonicity along the axial and the affine-radial directions, of the first eigenfunctions of the Zaremba problem for the Laplace operator on annular domains. These fine geometric properties, together with the shape calculus, help us to prove that the first eigenvalue is strictly decreasing as the inner ball moves towards the boundary of the outer ball.
Cite
@article{arxiv.2009.13967,
title = {A shape variation result via the geometry of eigenfunctions},
author = {T. V. Anoop and K. Ashok Kumar and S Kesavan},
journal= {arXiv preprint arXiv:2009.13967},
year = {2021}
}
Comments
21 pages, 3 figures