Quasilinear elliptic equations with singular quadratic growth terms
Fuente:
arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909731927359488 |
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| author | Boccardo, Lucio Leonori, Tommaso Orsina, Luigi Petitta, Francesco |
| author_facet | Boccardo, Lucio Leonori, Tommaso Orsina, Luigi Petitta, Francesco |
| contents | In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in $Ω$,}\newline \hfill u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} $$ where $Ω$ is a bounded open set of $\mathbb{R}^N$, $g\geq 0 $ is a function in some Lebesgue space, and $γ>0$. We prove both existence and nonexistence of solutions depending on the value of $γ$ and on the size of $g$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07695 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quasilinear elliptic equations with singular quadratic growth terms Boccardo, Lucio Leonori, Tommaso Orsina, Luigi Petitta, Francesco Analysis of PDEs In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -Δu + \frac{|\nabla u|^2}{(1-u)^γ}=g & \mbox{in $Ω$,}\newline \hfill u=0 \hfill & \mbox{on $\partialΩ$,} \end{cases} $$ where $Ω$ is a bounded open set of $\mathbb{R}^N$, $g\geq 0 $ is a function in some Lebesgue space, and $γ>0$. We prove both existence and nonexistence of solutions depending on the value of $γ$ and on the size of $g$. |
| title | Quasilinear elliptic equations with singular quadratic growth terms |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.07695 |