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arXiv · 1206.1278

Geometrical structure of Laplacian eigenfunctions

Denis S. Grebenkov·Binh-Thanh Nguyen
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Abstract

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.

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Denis S. Grebenkov, Binh-Thanh Nguyen. 2012-06-06. Geometrical structure of Laplacian eigenfunctions. https://doi.org/10.1137/120880173

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