Singular elliptic equations having a gradient term with natural growth
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arXiv
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| Format: | Preprint |
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2024
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| author | Ferone, A. Mercaldo, A. de León, S. Segura |
| author_facet | Ferone, A. Mercaldo, A. de León, S. Segura |
| contents | We study a class of Dirichlet boundary value problems whose prototype is \begin{equation}\label{1.2abs}
\left\{\begin{array}{ll}
-Δ_p u =h(u)|\nabla u|^p+u^{q-1}+f(x)\, &\quad\hbox{in } \ Ω\,,\\ u\ge 0\,,&{\quad\hbox{in } \ Ω}\\ u = 0\,&\quad\hbox{on }\partial Ω\,,\end{array}\right. \end{equation} where $Ω$ an open bounded subset of $\mathbb R^N$, $0<q<1$, $1<p<N$, $h$ is a continuous function and $f$ belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term and a first order term with natural growth in the gradient. A priori estimates and existence results are proved depending on the summability of the datum $f$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2401_06237 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Singular elliptic equations having a gradient term with natural growth Ferone, A. Mercaldo, A. de León, S. Segura Analysis of PDEs 35B25, 35J25 We study a class of Dirichlet boundary value problems whose prototype is \begin{equation}\label{1.2abs} \left\{\begin{array}{ll} -Δ_p u =h(u)|\nabla u|^p+u^{q-1}+f(x)\, &\quad\hbox{in } \ Ω\,,\\ u\ge 0\,,&{\quad\hbox{in } \ Ω}\\ u = 0\,&\quad\hbox{on }\partial Ω\,,\end{array}\right. \end{equation} where $Ω$ an open bounded subset of $\mathbb R^N$, $0<q<1$, $1<p<N$, $h$ is a continuous function and $f$ belongs to a suitable Lebesgue space. The main features of this problem are the presence of a singular term and a first order term with natural growth in the gradient. A priori estimates and existence results are proved depending on the summability of the datum $f$. |
| title | Singular elliptic equations having a gradient term with natural growth |
| topic | Analysis of PDEs 35B25, 35J25 |
| url | https://arxiv.org/abs/2401.06237 |