A shape variation result via the geometry of eigenfunctions
| Autor: | S. Kesavan, K. Ashok Kumar, T. V. Anoop |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
35B06
35B07 35B50 35B51 35Q93 49Q10 58J70 Applied Mathematics Mathematical analysis Monotonic function Eigenfunction Mathematics - Analysis of PDEs Optimization and Control (math.OC) Shape calculus FOS: Mathematics Ball (mathematics) Mathematics - Optimization and Control Laplace operator Analysis Eigenvalues and eigenvectors Analysis of PDEs (math.AP) Mathematics |
| Zdroj: | Journal of Differential Equations. 298:430-462 |
| ISSN: | 0022-0396 |
| Popis: | 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. 21 pages, 3 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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