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arXiv · 2507.21962

Pohozaev-like identity for the regional fractional laplacian

Sidy M. Djitte
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Abstract

We establish a new integration by parts formula for the regional fractional laplacian $(-\Delta)^s_\Omega$ in bounded open sets of class $C^2$. 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.

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Sidy M. Djitte. 2025-07-29. Pohozaev-like identity for the regional fractional laplacian. https://arxiv.org/abs/2507.21962

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