【114/12/11】16:20-17:10 陳志漢 助理教授 (國立中山大學應用數學系)
發佈日期 :
2025-12-01
| Colloquium | |
|
|
|
| Time | 2025-12-11 16:20-17:10 |
| Venue | 數學館1樓3174教室 |
| Speaker | 陳志漢 助理教授 (國立中山大學應用數學系) |
| Title | Shape Optimisation for Eigenvalues of the Laplace Operator |
| Abstract | Lord Rayleigh conjectured in 1877 that the disc has the lowest principal frequency among fixed membranes with a given area, where the principal frequency corresponds to the first eigenvalue of the Laplacian with Dirichlet boundary condition. This conjecture was proven independently by Faber and Krahn in the 1920s, a result now known as the Rayleigh-Faber-Krahn inequality. Such problem is known as an extremal eigenvalue problem or a shape optimisation problem, where one aims to minimise or maximise the k-th eigenvalue of a differential operator subject to a geometric constraint. In this talk, we will survey known results about extremal eigenvalues of the Laplacian for various boundary conditions. Time permitting, we will discuss a local shape optimisation problem for Steklov eigenvalues using perturbation methods. |
|
|
|