Výsledky vyhledávání - "Courant theorem"

Courant-sharp property for Dirichlet eigenfunctions on the Möbius strip

Autor: Pierre Bérard, Bernard Helffer, Rola Kiwan

Publikováno v: Portugaliae Mathematica
Portugaliae Mathematica, European Mathematical Society Publishing House, 2021, 78 (1), pp.1--41

The question of determining for which eigenvalues there exists an eigenfunction which has the same number of nodal domains as the label of the associated eigenvalue (Courant-sharp property) was motivated by the analysis of minimal spectral partitions

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23269f1b4be533287c7954d7dde5b771
https://doi.org/10.4171/pm/2059

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Akademický článek

Introduction to some conjectures for spectral minimal partitions

Autor: B. Helffer

Publikováno v: Journal of the Egyptian Mathematical Society, Vol 19, Iss 1, Pp 45-51 (2011)

Given a bounded open set Ω in Rn (or in a Riemannian manifold) and a partition of Ω by k open sets Dj, we consider the quantity maxjλ(Dj) where λ(Dj) is the ground state energy of the Dirichlet realization of the Laplacian in Dj. If we denote by

Externí odkaz: https://doaj.org/article/fd59dd477ef748579fc6703257b1b455

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Courant-sharp eigenvalues of compact flat surfaces: Klein bottles and cylinders

Autor: Rola Kiwan, Bernard Helffer, Pierre Bérard

Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2022, 150, pp.439--453

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::913c92bb7f149e3007dc0d3e7acdb8f1
https://hal.archives-ouvertes.fr/hal-02937338

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Akademický článek

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On nodal domains in Euclidean balls

Autor: Mikael Persson Sundqvist, Bernard Helffer

Publikováno v: Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society, American Mathematical Society, 2016, 144, pp.4777-4791. ⟨10.1090/proc/13098⟩

\AA. Pleijel (1956) has proved that in the case of the Laplacian with Dirichlet condition, the equality in the Courant nodal theorem (Courant sharp situation) can only be true for a finite number of eigenvalues when the dimension is $\geq 2$. Recentl

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f57928c08276f15254c7adac21ed322f
https://doi.org/10.1090/proc/13098

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The weak Pleijel theorem with geometric control

Autor: Pierre Bérard, Bernard Helffer

Publikováno v: Journal of Spectral Theory
Journal of Spectral Theory, European Mathematical Society, 2016, 6 (4), pp.717--733

Let $\Omega\subset \mathbb R^d\,, d\geq 2$, be a bounded open set, and denote by $\lambda\_j(\Omega), j\geq 1$, the eigenvalues of the Dirichlet Laplacian arranged in nondecreasing order, with multiplicities. The weak form of Pleijel's theorem states

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::e60eee4d615c466d16aed5c0c8579044
https://doi.org/10.4171/jst/138

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Akademický článek

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Courant-sharp eigenvalues of a two-dimensional torus

Autor: Corentin Léna

Publikováno v: Comptes Rendus. Mathématique
Comptes Rendus. Mathématique, 2015, 353 (6), pp.535-539. ⟨10.1016/j.crma.2015.03.014⟩
Comptes Rendus. Mathématique, Académie des sciences (Paris), 2015, 353 (6), pp.535-539. ⟨10.1016/j.crma.2015.03.014⟩

Version abrégée pour publication - Shortened published version; International audience; In this paper, we determine, in the case of the Laplacian on the flat two-dimensional torus (R/Z) 2 , all the eigenvalues having an eigenfunction which satisfie

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a8d2c9b981108259de85115fc18b9944
https://doi.org/10.1016/j.crma.2015.03.014

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Dirichlet eigenfunctions in the cube, sharpening the Courant nodal inequality

Autor: Bernard Helffer, Rola Kiwan

Publikováno v: 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

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

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bdf316ab0ebd85607a2a81ce204c8d5e
https://doi.org/10.4171/175-1/17

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Courant-sharp eigenvalues for the equilateral torus, and for the equilateral triangle

Autor: Bernard Helffer, Pierre Bérard

Publikováno v: Letters in Mathematical Physics
Letters in Mathematical Physics, Springer Verlag, 2016, 106 (12), pp.1729--1789

We address the question of determining the eigenvalues $\lambda\_n$ (listed in nondecreasing order, with multiplicities) for which Courant's nodal domain theorem is sharp i.e., for which there exists an associated eigenfunction with $n$ nodal domains

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::2fc002a0843356c60d4dbeb860c9f2b8
https://hal.archives-ouvertes.fr/hal-01120958v3/document

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