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arXiv · 2608.05433

Truncations for fractional Laplacians

Egor Ignatev·Alexander I. Nazarov·Pavel Nichitenko·Artur Tursunbaev
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Abstract

Let $\Omega\subset\mathbb R^n$ be a bounded Lipschitz domain. We prove and widely generalize a conjecture of A.\,I.~Nazarov \cite{Naz21}: for $s\in(1,\frac 32)$ the quadratic form $Q^{\rm SP}_s[u]$ of the spectral fractional Dirichlet Laplacian strictly increases under the map $u\mapsto|u|$ provided $u\in\tilde H^s(\Omega)$ changes sign in $\Omega$.

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Egor Ignatev, Alexander I. Nazarov, Pavel Nichitenko, Artur Tursunbaev. 2026-08-05. Truncations for fractional Laplacians. https://arxiv.org/abs/2608.05433

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