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

• Autorzy: Claudia Anedda , Fabrizio Cuccu
• Języki publikacji: EN

Abstrakty

EN

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 $∫_{D₀} ρdx = αγ + β(|D₀|-γ)$ 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.

Kategorie tematyczne

• 35J40: Boundary value problems for higher-order elliptic equations
• 47A75: Eigenvalue problems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Applicationes Mathematicae
• Rocznik: 2015
• Tom: 42
• Numer: 2-3
• Strony: 183-191

Daty

wydano

2015

Twórcy

autor

Claudia Anedda

• Mathematics and Computer Science Department, University of Cagliari, 09124 Cagliari (CA), Italy

autor

Fabrizio Cuccu

• Mathematics and Computer Science Department, University of Cagliari, 09124 Cagliari (CA), Italy

Identyfikatory

DOI

10.4064/am42-2-5