TY - JOUR

T1 - On comparison of fractional Laplacians

AU - Nazarov, Alexander I.

N1 - Publisher Copyright: © 2022 Elsevier Ltd

PY - 2022/5

Y1 - 2022/5

N2 - For s>−1, s∉N0, we compare two natural types of fractional Laplacians (−Δ)s, namely, the restricted Dirichlet and the spectral Neumann ones. We show that the quadratic form of their difference taken on the space H˜s(Ω) is positive or negative depending on whether the integer part of s is even or odd. For s∈(0,1) and convex domains we prove also that the difference of these operators is positivity preserving on H˜s(Ω). This paper complements (Musina and Nazarov, 2014; 2016) where similar statements were proved for the spectral Dirichlet and the restricted Dirichlet fractional Laplacians.

AB - For s>−1, s∉N0, we compare two natural types of fractional Laplacians (−Δ)s, namely, the restricted Dirichlet and the spectral Neumann ones. We show that the quadratic form of their difference taken on the space H˜s(Ω) is positive or negative depending on whether the integer part of s is even or odd. For s∈(0,1) and convex domains we prove also that the difference of these operators is positivity preserving on H˜s(Ω). This paper complements (Musina and Nazarov, 2014; 2016) where similar statements were proved for the spectral Dirichlet and the restricted Dirichlet fractional Laplacians.

KW - Nonlocal differential operators

KW - Restricted fractional Laplacian

KW - Spectral fractional Laplacians

UR - http://www.scopus.com/inward/record.url?scp=85123887561&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/3e5f3a2b-d26d-345f-911c-bd64513b0931/

U2 - 10.1016/j.na.2022.112790

DO - 10.1016/j.na.2022.112790

M3 - Article

AN - SCOPUS:85123887561

VL - 218

JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

SN - 0362-546X

M1 - 112790

ER -