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

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].
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: http://hdl.handle.net/2108/173863
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