Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk

Cuccu, Fabrizio; Anedda, Claudia

doi:10.4064/am42-2-5

Let D0={x∈R2:0<|x|<1} be the unit punctured disk. We consider the first eigenvalue λ1(ρ) of the problem Δ2u=λρu 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 ∫D0ρdx=αγ+β(|D0|−γ) 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.

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Titolo:	Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk
Autori:	CUCCU, FABRIZIO ANEDDA, CLAUDIA
Data di pubblicazione:	2015
Rivista:	APPLICATIONES MATHEMATICAE
Handle:	http://hdl.handle.net/11584/130086
Tipologia:	1.1 Articolo in rivista

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http://hdl.handle.net/11584/130086

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