A shape variation result via the geometry of eigenfunctions

[摘要] 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 a Zaremba problem for the Laplace operator on annular domains. Together with the shape calculus, these fine geometric properties help us to prove that the first eigenvalue is strictly decreasing as the inner ball moves towards the boundary of the outer ball. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Geometry of the first eigenfunctions;Foliated Schwarz symmetry;Shape derivative;Monotonicity of the first eigenvalue;Zaremba problem;Torsional rigidity