Pohozaev-like identity for the regional fractional laplacian

2025/07/29 by Sidy M. Djitte, Djitte, Sidy M.
#math.AP

paper · pdf · doi:10.48550/arxiv.2507.21962

Abstract

We establish a new integration by parts formula for the regional fractional laplacian (-Δ)^s_Ω in bounded open sets of class C². As a direct application, we prove that weak solutions to the corresponding Dirichlet problem satisfy a Pohozaev-like identity with an explicit remainder term. We apply the later to eigenvalue problems in the unit ball and discuss its potential use in establishing boundary-type unique continuation properties.

Citations

• A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
• The Pohozaev Identity for the Fractional Laplacian

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