Boundary estimates for singular elliptic problems involving a gradient term
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912531160760320 |
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| author | Le, Phuong |
| author_facet | Le, Phuong |
| contents | We study the behavior of weak solutions to the singular quasilinear elliptic problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$, in a bounded domain with the Dirichlet boundary condition, where $p>1$, $γ>0$, $0<q\le p$, $\vartheta\ge0$ and $f:[0,+\infty)\to\mathbb{R}$ is a locally Lipschitz continuous function. We obtain a precise estimate for directional derivatives of positive solutions in a neighborhood of the boundary. We also deduce the symmetry of positive solutions to the problem in a bounded symmetric convex domain. Our results are new even in the case $p=2$ and $\vartheta=0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07360 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Boundary estimates for singular elliptic problems involving a gradient term Le, Phuong Analysis of PDEs We study the behavior of weak solutions to the singular quasilinear elliptic problem $-Δ_p u + \vartheta |\nabla u|^q = \frac{1}{u^γ} + f(u)$, in a bounded domain with the Dirichlet boundary condition, where $p>1$, $γ>0$, $0<q\le p$, $\vartheta\ge0$ and $f:[0,+\infty)\to\mathbb{R}$ is a locally Lipschitz continuous function. We obtain a precise estimate for directional derivatives of positive solutions in a neighborhood of the boundary. We also deduce the symmetry of positive solutions to the problem in a bounded symmetric convex domain. Our results are new even in the case $p=2$ and $\vartheta=0$. |
| title | Boundary estimates for singular elliptic problems involving a gradient term |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.07360 |