An equation involving the 1-Laplacian and a singular nonlinearity
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911726160576512 |
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| author | da Silva, Genival |
| author_facet | da Silva, Genival |
| contents | We prove existence of solutions to a nonlinear degenerate elliptic equation of the form
\[ \begin{cases} -Δ_{1} u+ \frac{|D u|}{(1-u)^γ}=g & \mbox{in $Ω$,}\\ u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases}
\] in a suitable sense, where $Ω$ is a bounded open set of $\mathbb{R}^n$, $γ>0$ is a fixed parameter, $g\geq 0 $ is a function in some Lebesgue space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_29175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | An equation involving the 1-Laplacian and a singular nonlinearity da Silva, Genival Analysis of PDEs We prove existence of solutions to a nonlinear degenerate elliptic equation of the form \[ \begin{cases} -Δ_{1} u+ \frac{|D u|}{(1-u)^γ}=g & \mbox{in $Ω$,}\\ u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} \] in a suitable sense, where $Ω$ is a bounded open set of $\mathbb{R}^n$, $γ>0$ is a fixed parameter, $g\geq 0 $ is a function in some Lebesgue space. |
| title | An equation involving the 1-Laplacian and a singular nonlinearity |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2605.29175 |