Local integration by parts and Pohozaev identities for higher order\n fractional Laplacians

2014/06/04 by Xavier Ros‐Oton, Joaquim Serra, Ros-Oton, Xavier +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1406.1107

openalex publication_date 2014/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an integration by parts formula in bounded domains for the\nhigher order fractional Laplacian (-\Δ)^s with s>1. We also obtain the\nPohozaev identity for this operator. Both identities involve local boundary\nterms, and they extend the identities obtained by the authors in the case\ns\∈(0,1).\n As an immediate consequence of these results, we obtain a unique continuation\nproperty for the eigenfunctions (-\Δ)^s\φ=\λ\φ in \Ω,\n\φ\≡0 in mathbb Rⁿ\∖\Ω.\n

Citations

• The Pohozaev Identity for the Fractional Laplacian
• Exact Controllability, Stabilization and Perturbations for Distributed Systems
• Regularity of the obstacle problem for a fractional power of the laplace operator
• The existence of weak solutions with prescribed singular behavior for a conformally invariant scalar equation

Cited by

• The higher-order fractional Schrödinger equation with nonlinear local perturbations: Uniqueness

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