Geometrical structure of Laplacian eigenfunctions
- Resource Type
- Working Paper
- Authors
- Grebenkov, Denis S.; Nguyen, Binh-Thanh
- Source
- SIAM Reviews 55, 601-667 (2013)
- Subject
- Mathematics - Analysis of PDEs
Mathematical Physics
Quantum Physics
35J05, 35Pxx, 49Rxx, 51Pxx
- Language
We summarize the properties of eigenvalues and eigenfunctions of the Laplace operator in bounded Euclidean domains with Dirichlet, Neumann or Robin boundary condition. We keep the presentation at a level accessible to scientists from various disciplines ranging from mathematics to physics and computer sciences. The main focus is put onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions.
Comment: 70 pages, 22 figures