Elliptic equations with a singular drift from a weak Morrey space
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866929577861840896 |
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| author | Chernobai, Misha Shilkin, Timofey |
| author_facet | Chernobai, Misha Shilkin, Timofey |
| contents | In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift $b$ satisfying $\operatorname{div} b\le 0$ in $Ω$. We assume $b$ belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where $r=\sqrt{x_1^2+x_2^2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_10909 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Elliptic equations with a singular drift from a weak Morrey space Chernobai, Misha Shilkin, Timofey Analysis of PDEs In this paper we prove the existence and uniqueness of weak solutions to the Dirichlet problem for an elliptic equation with a drift $b$ satisfying $\operatorname{div} b\le 0$ in $Ω$. We assume $b$ belongs to some weak Morrey class which includes in the 3D case, in particular, drifts having a singularity along the axis $x_3$ with the asymptotic $b(x)\sim c/r$, where $r=\sqrt{x_1^2+x_2^2}$. |
| title | Elliptic equations with a singular drift from a weak Morrey space |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2208.10909 |