On mixed local-nonlocal problems with Hardy potential
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866914942887657472 |
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| author | Biagi, Stefano Esposito, Francesco Montoro, Luigi Vecchi, Eugenio |
| author_facet | Biagi, Stefano Esposito, Francesco Montoro, Luigi Vecchi, Eugenio |
| contents | In this paper we study the effect of the Hardy potential on existence, uniqueness and optimal summability of solutions of the mixed local-nonlocal elliptic problem $$-Δu + (-Δ)^s u - γ\frac{u}{|x|^2}=f \text{ in } Ω, \ u=0 \text{ in } \mathbb{R}^n \setminus Ω,$$ where $Ω$ is a bounded domain in $\mathbb{R}^n$ containing the origin and $γ> 0$. In particular, we will discuss the existence, non-existence and uniqueness of solutions in terms of the summability of $f$ and of the value of the parameter $γ$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_06763 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On mixed local-nonlocal problems with Hardy potential Biagi, Stefano Esposito, Francesco Montoro, Luigi Vecchi, Eugenio Analysis of PDEs In this paper we study the effect of the Hardy potential on existence, uniqueness and optimal summability of solutions of the mixed local-nonlocal elliptic problem $$-Δu + (-Δ)^s u - γ\frac{u}{|x|^2}=f \text{ in } Ω, \ u=0 \text{ in } \mathbb{R}^n \setminus Ω,$$ where $Ω$ is a bounded domain in $\mathbb{R}^n$ containing the origin and $γ> 0$. In particular, we will discuss the existence, non-existence and uniqueness of solutions in terms of the summability of $f$ and of the value of the parameter $γ$. |
| title | On mixed local-nonlocal problems with Hardy potential |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2407.06763 |