Minimising convex combinations of low eigenvalues

Mette Iversen; Dario Mazzoleni

ESAIM: Control, Optimisation and Calculus of Variations (2014)

  • Volume: 20, Issue: 2, page 442-459
  • ISSN: 1292-8119

Abstract

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We consider the variational problem         inf{αλ1(Ω) + βλ2(Ω) + (1 − α − β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.

How to cite

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Iversen, Mette, and Mazzoleni, Dario. "Minimising convex combinations of low eigenvalues." ESAIM: Control, Optimisation and Calculus of Variations 20.2 (2014): 442-459. <http://eudml.org/doc/272932>.

@article{Iversen2014,
abstract = {We consider the variational problem         inf\{αλ1(Ω) + βλ2(Ω) + (1 − α − β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1\}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.},
author = {Iversen, Mette, Mazzoleni, Dario},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {eigenvalues; Dirichlet–Laplacian; shape optimization; Dirichlet-Laplacian},
language = {eng},
number = {2},
pages = {442-459},
publisher = {EDP-Sciences},
title = {Minimising convex combinations of low eigenvalues},
url = {http://eudml.org/doc/272932},
volume = {20},
year = {2014},
}

TY - JOUR
AU - Iversen, Mette
AU - Mazzoleni, Dario
TI - Minimising convex combinations of low eigenvalues
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2014
PB - EDP-Sciences
VL - 20
IS - 2
SP - 442
EP - 459
AB - We consider the variational problem         inf{αλ1(Ω) + βλ2(Ω) + (1 − α − β)λ3(Ω) | Ω open in ℝn, |Ω| ≤ 1}, for α, β ∈ [0, 1], α + β ≤ 1, where λk(Ω) is the kth eigenvalue of the Dirichlet Laplacian acting in L2(Ω) and |Ω| is the Lebesgue measure of Ω. We investigate for which values of α, β every minimiser is connected.
LA - eng
KW - eigenvalues; Dirichlet–Laplacian; shape optimization; Dirichlet-Laplacian
UR - http://eudml.org/doc/272932
ER -

References

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  14. [14] B. Osting and C.-Y. Kao, Minimal convex combinations of three sequential Laplace−Dirichlet eigenvalues, Appl. Math. Optim. 69 (2014) 123–139. Zbl1305.49066MR3162497
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