Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

Autor: Matteo Dalla Riva, Virginie Bonnaillie-Noël, Paolo Musolino, Marc Dambrine

For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula present

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::15326a04de159403d35bc89bb6e10c13
http://hdl.handle.net/10447/546027

Minimal partitions for $p$-norms of eigenvalues

Autor: Beniamin Bogosel, Virginie Bonnaillie-Noël

Publikováno v: Interfaces and Free Boundaries
Interfaces and Free Boundaries, European Mathematical Society, 2018, 20, pp.129-163

International audience; In this article we are interested in studying partitions of the square, the disk and the equilateral triangle which minimize a p-norm of eigenvalues of the Dirichlet-Laplace operator. The extremal case of the infinity norm, wh

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::85e0b734241b88d800938683d34ee755
https://doi.org/10.4171/ifb/399

A Dirichlet problem for the Laplace operator in a domain with a small hole close to the boundary

Autor: Paolo Musolino, Virginie Bonnaillie-Noël, Matteo Dalla Riva, Marc Dambrine

Publikováno v: Journal de Mathématiques Pures et Appliquées
Journal de Mathématiques Pures et Appliquées, Elsevier, 2018, ⟨10.1016/j.matpur.2018.01.004⟩
Journal de Mathématiques Pures et Appliquées, 2018, ⟨10.1016/j.matpur.2018.01.004⟩

We study the Dirichlet problem in a domain with a small hole close to the boundary. To do so, for each pair $\boldsymbol\varepsilon = (\varepsilon_1, \varepsilon_2 )$ of positive parameters, we consider a perforated domain $\Omega_{\boldsymbol\vareps

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0cb1540ab60f3f40d3d4a97c8578df56
http://hdl.handle.net/10278/3723515

Curvature induced magnetic bound states: towards the tunneling effect for the ellipse

Autor: Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond

This article is devoted to the semiclassical analysis of the magnetic Laplacian on a smooth domain of the plane carrying Neumann boundary conditions. We provide WKB expansions of the eigenfunctions in generic situations. We also explain and illustrat

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04aaafc25461c73c522378f6b1af9ab3
https://hal.archives-ouvertes.fr/hal-01404924

On the eigenvalues of Aharonov–Bohm operators with varying poles

Autor: Susanna Terracini, Virginie Bonnaillie-Noël, Benedetta Noris, Manon Nys

Publikováno v: Analysis & PDE
Analysis & PDE, Mathematical Sciences Publishers, 2014, 7 (6), pp.1365-1395. 〈10.2140/apde.2014.7.1365〉
Analysis & PDE, Mathematical Sciences Publishers, 2014, 7 (6), pp.1365-1395. ⟨10.2140/apde.2014.7.1365⟩
Analysis & PDE, 2014, 7 (6), pp.1365-1395. ⟨10.2140/apde.2014.7.1365⟩
Anal. PDE 7, no. 6 (2014), 1365-1395

We consider a magnetic operator of Aharonov-Bohm type with Dirichlet boundary conditions in a planar domain. We analyse the behavior of its eigenvalues as the singular pole moves in the domain. For any value of the circulation we prove that the k-th

Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::00b43d866e7890585f01fe2dbd811901
https://doi.org/10.2140/apde.2014.7.1365