Geometrical Structure of Laplacian Eigenfunctions

• Autores: D. S. Grebenkov, B. T. Nguyen
• Localización: SIAM Review, ISSN 0036-1445, Vol. 55, Nº. 4, 2013, págs. 601-667
• Idioma: inglés
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• Resumen

  • 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 placed onto multiple intricate relations between the shape of a domain and the geometrical structure of eigenfunctions