Truncations for fractional Laplacians
Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko, Artur Tursunbaev
Abstract
Let Ω⊂ Rn be a bounded Lipschitz domain. We prove and widely generalize a conjecture of A.\,I.~Nazarov Naz21: for s∈(1, 32) the quadratic form Q SPs[u] of the spectral fractional Dirichlet Laplacian strictly increases under the map u|u| provided u∈ Hs(Ω) changes sign in Ω.
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