Existence of solutions for $1-$laplacian problems with singular first order terms
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910814905040896 |
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| author | Balducci, Francesco |
| author_facet | Balducci, Francesco |
| contents | We prove existence of solutions to the following problem
\begin{equation*}
\begin{cases}
-Δ_1 u +g(u)|Du|=h(u)f & \text{in $Ω$,}
\\ u=0 & \text{on $\partialΩ$,}
\end{cases}
\end{equation*}
where $Ω\subset \mathbb{R}^N$, with $N\ge2$, is an open and bounded set with Lipschitz boundary, $g$ is a continuous and positive function which possibly blows up at the origin and bounded at infinity and $h$ is a continuous and nonnegative function bounded at infinity (possibly blowing up at the origin) and finally $0 \le f \in L^N(Ω)$. As a by-product, this paper extends the results found where $g$ is a continuous and bounded function. \\We investigate the interplay between $g$ and $h$ in order to have existence of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_03050 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of solutions for $1-$laplacian problems with singular first order terms Balducci, Francesco Analysis of PDEs 35J25, 35J60, 35J75 We prove existence of solutions to the following problem \begin{equation*} \begin{cases} -Δ_1 u +g(u)|Du|=h(u)f & \text{in $Ω$,} \\ u=0 & \text{on $\partialΩ$,} \end{cases} \end{equation*} where $Ω\subset \mathbb{R}^N$, with $N\ge2$, is an open and bounded set with Lipschitz boundary, $g$ is a continuous and positive function which possibly blows up at the origin and bounded at infinity and $h$ is a continuous and nonnegative function bounded at infinity (possibly blowing up at the origin) and finally $0 \le f \in L^N(Ω)$. As a by-product, this paper extends the results found where $g$ is a continuous and bounded function. \\We investigate the interplay between $g$ and $h$ in order to have existence of solutions. |
| title | Existence of solutions for $1-$laplacian problems with singular first order terms |
| topic | Analysis of PDEs 35J25, 35J60, 35J75 |
| url | https://arxiv.org/abs/2502.03050 |