We study the spectrum of one dimensional integral operators in bounded real intervals of length 2L, for value of L large. The integral operators are obtained by linearizing a non local evolution equation for a non conserved order parameter describing the phases of a fluid. We prove a Perron–Frobenius theorem showing that there is an isolated, simple minimal eigenvalue strictly positive for L finite, going to zero exponentially fast in L. We lower bound, uniformly on L, the spectral gap by applying a generalization of the Cheeger's inequality. These results are needed for deriving spectral properties for non local Cahn–Hilliard type of equations in problems of interface dynamics, see [16].
Orlandi, E., Liverani, C. (2017). Spectral properties of integral operators in bounded, large intervals. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 450(1), 330-350 [10.1016/j.jmaa.2017.01.032].
Spectral properties of integral operators in bounded, large intervals
LIVERANI, CARLANGELO
2017-01-01
Abstract
We study the spectrum of one dimensional integral operators in bounded real intervals of length 2L, for value of L large. The integral operators are obtained by linearizing a non local evolution equation for a non conserved order parameter describing the phases of a fluid. We prove a Perron–Frobenius theorem showing that there is an isolated, simple minimal eigenvalue strictly positive for L finite, going to zero exponentially fast in L. We lower bound, uniformly on L, the spectral gap by applying a generalization of the Cheeger's inequality. These results are needed for deriving spectral properties for non local Cahn–Hilliard type of equations in problems of interface dynamics, see [16].File | Dimensione | Formato | |
---|---|---|---|
enza.pdf
solo utenti autorizzati
Licenza:
Copyright dell'editore
Dimensione
431.49 kB
Formato
Adobe PDF
|
431.49 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.