Geometrical Structure of Laplacian Eigenfunctions
By Denis S. Grebenkov, Binh T. Nguyen. SIAM Review, 2012
363 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/3007e2d602e79c1a2a1aebeffc07405addaff0ba
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In Computational Theory and Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Minimal supersolutions for BSDEs with singular terminal condition and application to optimal position targeting (2015, neutral): “See [14] for details.”
- On vanishing near corners of transmission eigenfunctions (2017, background): “ contained in a subdomain which is a fraction of the total domain. Considerable effort has been spent on the nodal sets and localization in the classical spectral theory. We refer to the recent survey [19]. For the curious, we mention briefly basic facts about them, all of which are completely open fo”
- Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications (2015, background): “As pointed out in [10,11], much more literatures concern the principal eigenvalue for elliptic operators with Dirichlet or Robin boundary conditions; see [5–8,16,17,20,21,30,38, 46,47,56] among many others; in particular, in an extensive survey paper [32], Grebenkov and Nyuyen summarized the very re”