DOI

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.

Original languageEnglish
Article number112790
JournalNonlinear Analysis, Theory, Methods and Applications
Volume218
DOIs
StatePublished - May 2022

    Research areas

  • Nonlocal differential operators, Restricted fractional Laplacian, Spectral fractional Laplacians

    Scopus subject areas

  • Analysis
  • Applied Mathematics

ID: 93227507