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].
2017
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/07 - FISICA MATEMATICA
English
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].
Orlandi, E; Liverani, C
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/173863
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