The Pohozaev identity for mixed local-nonlocal operator
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915724463702016 |
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| author | Biswas, Anup |
| author_facet | Biswas, Anup |
| contents | In this article we prove the Pohozaev identity for the semilinear Dirichlet problem of the form $-Δu + a(-Δ)^s u = f(u)$ in $Ω$, and $u=0$ in $Ω^c$, where $a$ is a non-negative constant and $Ω$ is a bounded $C^2$ domain. We also establish similar identity for systems of equations. As applications of this identity, we deduce a unique continuation property of eigenfunctions and also the nonexistence of nontrivial solutions in star-shaped domains under suitable condition on $f$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_16661 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Pohozaev identity for mixed local-nonlocal operator Biswas, Anup Analysis of PDEs 35R11, 35A01 In this article we prove the Pohozaev identity for the semilinear Dirichlet problem of the form $-Δu + a(-Δ)^s u = f(u)$ in $Ω$, and $u=0$ in $Ω^c$, where $a$ is a non-negative constant and $Ω$ is a bounded $C^2$ domain. We also establish similar identity for systems of equations. As applications of this identity, we deduce a unique continuation property of eigenfunctions and also the nonexistence of nontrivial solutions in star-shaped domains under suitable condition on $f$. |
| title | The Pohozaev identity for mixed local-nonlocal operator |
| topic | Analysis of PDEs 35R11, 35A01 |
| url | https://arxiv.org/abs/2410.16661 |