Pohozaev-like identity for the regional fractional laplacian
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918123769167872 |
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| author | Djitte, Sidy M. |
| author_facet | Djitte, Sidy M. |
| contents | We establish a new integration by parts formula for the regional fractional laplacian $(-Δ)^s_Ω$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_21962 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Pohozaev-like identity for the regional fractional laplacian Djitte, Sidy M. Analysis of PDEs We establish a new integration by parts formula for the regional fractional laplacian $(-Δ)^s_Ω$ 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. |
| title | Pohozaev-like identity for the regional fractional laplacian |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2507.21962 |