T. V. Anoop, K. Ashok Kumar, Srinivasan Kesavan
Published 2020-09-29Version 1
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.
Comments: 21 pages, 3 figures
On the strict monotonicity of the first eigenvalue of the $p$-Laplacian on annuli
Minimization of the first eigenvalue for the Lamé system
Shape derivative of the first eigenvalue of the 1-Laplacian
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