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.

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

CUCCU, FABRIZIO;ANEDDA, CLAUDIA
2015

Abstract

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.
File in questo prodotto:
File Dimensione Formato  
Symmetry breaking in the minimization of the first eigenvalue for the composite clamped punctured disk.pdf

Solo gestori archivio

Tipologia: versione editoriale
Dimensione 257.13 kB
Formato Adobe PDF
257.13 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/130086
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact