We deal with the sharp asymptotic behaviour of eigenvalues of elliptic operators with varying mixed Dirichlet–Neumann boundary conditions. In case of simple eigenvalues, we compute explicitly the constant appearing in front of the expansion’s leading term. This allows inferring some remarkable consequences for Aharonov–Bohm eigenvalues when the singular part of the operator has two coalescing poles.
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DOI : 10.1051/cocv/2019022
Mots-clés : Mixed boundary conditions, asymptotics of eigenvalues, Aharonov–Bohm eigenvalues
@article{COCV_2020__26_1_A39_0,
author = {Abatangelo, L. and Felli, V. and L\'ena, C.},
title = {Eigenvalue variation under moving mixed {Dirichlet{\textendash}Neumann} boundary conditions and applications},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {26},
year = {2020},
doi = {10.1051/cocv/2019022},
mrnumber = {4116678},
zbl = {1446.35085},
language = {en},
url = {http://www.numdam.org/articles/10.1051/cocv/2019022/}
}
TY - JOUR AU - Abatangelo, L. AU - Felli, V. AU - Léna, C. TI - Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv/2019022/ DO - 10.1051/cocv/2019022 LA - en ID - COCV_2020__26_1_A39_0 ER -
%0 Journal Article %A Abatangelo, L. %A Felli, V. %A Léna, C. %T Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv/2019022/ %R 10.1051/cocv/2019022 %G en %F COCV_2020__26_1_A39_0
Abatangelo, L.; Felli, V.; Léna, C. Eigenvalue variation under moving mixed Dirichlet–Neumann boundary conditions and applications. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 39. doi : 10.1051/cocv/2019022. http://www.numdam.org/articles/10.1051/cocv/2019022/
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