Symmetry of bounded solutions to quasilinear elliptic equations in a half-space
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908567521460224 |
|---|---|
| author | Le, Phuong |
| author_facet | Le, Phuong |
| contents | Let $u$ be a bounded positive solution to the problem $-Δ_p u = f(u)$ in $\mathbb{R}^N_+$ with zero Dirichlet boundary condition, where $p>1$ and $f$ is a locally Lipschitz continuous function. Among other things, we show that if $f(\sup_{\mathbb{R}^N_+} u)=0$ and $f$ satisfies some other mild conditions, then $u$ depends only on $x_N$ and monotone increasing in the $x_N$-direction. Our result partially extends a classical result of Berestycki, Caffarelli and Nirenberg in 1993 to the $p$-Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_04804 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry of bounded solutions to quasilinear elliptic equations in a half-space Le, Phuong Analysis of PDEs Classical Analysis and ODEs 35J92, 35B06, 35A02, 34C25 Let $u$ be a bounded positive solution to the problem $-Δ_p u = f(u)$ in $\mathbb{R}^N_+$ with zero Dirichlet boundary condition, where $p>1$ and $f$ is a locally Lipschitz continuous function. Among other things, we show that if $f(\sup_{\mathbb{R}^N_+} u)=0$ and $f$ satisfies some other mild conditions, then $u$ depends only on $x_N$ and monotone increasing in the $x_N$-direction. Our result partially extends a classical result of Berestycki, Caffarelli and Nirenberg in 1993 to the $p$-Laplacian. |
| title | Symmetry of bounded solutions to quasilinear elliptic equations in a half-space |
| topic | Analysis of PDEs Classical Analysis and ODEs 35J92, 35B06, 35A02, 34C25 |
| url | https://arxiv.org/abs/2409.04804 |