Let D₀=x∈ ℝ²: 0<|x|<1 be the unit punctured disk. We consider the first eigenvalue λ₁(ρ ) of the problem Δ² u =λ ρ u in D₀ with Dirichlet boundary condition, where ρ is an arbitrary function that takes only two given values 0 < α < β and is subject to the constraint for a fixed 0 < γ < |D₀|. We will be concerned with the minimization problem ρ ↦ λ₁(ρ). We show that, under suitable conditions on α, β and γ, the minimizer does not inherit the radial symmetry of the domain.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-5,
author = {Claudia Anedda and Fabrizio Cuccu},
title = {Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk},
journal = {Applicationes Mathematicae},
volume = {42},
year = {2015},
pages = {183-191},
zbl = {1332.35236},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-5}
}
Claudia Anedda; Fabrizio Cuccu. Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk. Applicationes Mathematicae, Tome 42 (2015) pp. 183-191. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am42-2-5/