TY - JOUR

T1 - On the spectrum of two different fractional operators

AU - Servadei, Raffaella

AU - Valdinoci, Enrico

PY - 2014/1/1

Y1 - 2014/1/1

N2 - In this paper we deal with two non-local operators that are both well known and widely studied in the literature in connection with elliptic problems of fractional type. More precisely, for a fixed s ∈ (0,1) we consider the integral definition of the fractional Laplacian given by where c(n, s) is a positive normalizing constant, and another fractional operator obtained via a spectral definition, that is, where e i, λ i are the eigenfunctions and the eigenvalues of the Laplace operator -Δ in Ω with homogeneous Dirichlet boundary data, while a i represents the projection of u on the direction e i. The aim of this paper is to compare these two operators, with particular reference to their spectrum, in order to emphasize their differences.

AB - In this paper we deal with two non-local operators that are both well known and widely studied in the literature in connection with elliptic problems of fractional type. More precisely, for a fixed s ∈ (0,1) we consider the integral definition of the fractional Laplacian given by where c(n, s) is a positive normalizing constant, and another fractional operator obtained via a spectral definition, that is, where e i, λ i are the eigenfunctions and the eigenvalues of the Laplace operator -Δ in Ω with homogeneous Dirichlet boundary data, while a i represents the projection of u on the direction e i. The aim of this paper is to compare these two operators, with particular reference to their spectrum, in order to emphasize their differences.

UR - http://www.scopus.com/inward/record.url?scp=84904974819&partnerID=8YFLogxK

U2 - 10.1017/S0308210512001783

DO - 10.1017/S0308210512001783

M3 - Article

AN - SCOPUS:84904974819

VL - 144

SP - 831

EP - 855

JO - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH: SECTION A MATHEMATICS

JF - PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH: SECTION A MATHEMATICS

SN - 0308-2105

IS - 4

ER -