Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality
| Autor: | Bernard Helffer, Rola Kiwan |
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| Přispěvatelé: | Laboratoire de Mathématiques d'Orsay (LM-Orsay), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de Mathématiques Jean Leray (LMJL), Centre National de la Recherche Scientifique (CNRS)-Université de Nantes - UFR des Sciences et des Techniques (UN UFR ST), Université de Nantes (UN)-Université de Nantes (UN), American University in Dubai, J. Dittrich, H. Kowarik, A. Laptev |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Functional Analysis and Operator Theory for Quantum Physics. A Festschrift in Honor of Pavel Exner. J. Dittrich, H. Kowarik, A. Laptev. Functional Analysis and Operator Theory for Quantum Physics. A Festschrift in Honor of Pavel Exner., European Math. Society House, 2016 |
| DOI: | 10.4171/175-1/17 |
| Popis: | C'est juste un article à l'intérieur de ce volume.; International audience; This paper is devoted to the refined analysis of Courant's theorem for the Dirichlet Laplacian in a bounded open set. Starting from the work byÅbyÅ. Pleijel in 1956, many papers have investigated in which cases the inequality in Courant's theorem is an equality. All these results were established for open sets in R 2 or for surfaces like S 2 or T 2. The aim of the current paper is to look for the case of the cube in R 3. We will prove that the only eigenvalues of the Dirichlet Laplacian which are Courant sharp are the two first eigenvalues. |
| Databáze: | OpenAIRE |
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