Spectral stability under removal of small capacity sets and applications to Aharonov–Bohm operators
| Autor: | Laura Abatangelo, Luc Hillairet, Veronica Felli, Corentin Léna |
|---|---|
| Přispěvatelé: | Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO), Abatangelo, L, Felli, V, Hillairet, L, Lena, C |
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Mathematics::Analysis of PDEs
Aharonov-Bohm operators 01 natural sciences Dirichlet distribution Asymptotics of eigenvalues symbols.namesake Mathematics - Analysis of PDEs Dirichlet eigenvalue FOS: Mathematics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] Point (geometry) [MATH]Mathematics [math] 0101 mathematics MAT/05 - ANALISI MATEMATICA ComputingMilieux_MISCELLANEOUS Mathematical Physics Mathematics Aharonov–Bohm operators 010102 general mathematics Mathematical analysis Spectral stability Order (ring theory) Statistical and Nonlinear Physics Mathematics::Spectral Theory Eigenfunction Term (time) 010101 applied mathematics Asymptotics of eigenvalue Small capacity sets symbols Aharonov–Bohm operator Geometry and Topology Asymptotic expansion small capacity sets [MATH.MATH-SP]Mathematics [math]/Spectral Theory [math.SP] Analysis of PDEs (math.AP) |
| Zdroj: | Journal of Spectral Theory Journal of Spectral Theory, European Mathematical Society, 2019, 9 (2), pp.379-427. ⟨10.4171/JST/251⟩ |
| ISSN: | 1664-039X 1664-0403 |
| DOI: | 10.4171/JST/251⟩ |
| Popis: | We first establish a sharp relation between the order of vanishing of a Dirichlet eigenfunction at a point and the leading term of the asymptotic expansion of the Dirichlet eigenvalue variation, as a removed compact set concentrates at that point. Then we apply this spectral stability result to the study of the asymptotic behaviour of eigenvalues of Aharonov-Bohm operators with two colliding poles moving on an axis of symmetry of the domain. |
| Databáze: | OpenAIRE |
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