Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Unbounded Domains
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929299577110528 |
|---|---|
| author | Zhang, Weijun Zhang, Zhitao |
| author_facet | Zhang, Weijun Zhang, Zhitao |
| contents | In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Ampère systems for instance, considering
\begin{equation*}
\det(D^2u^i)=f^i(x,{\bf u},\nabla u^i), \ 1\leq i\leq m,
\end{equation*} over unbounded domains of various cases, including the whole spaces $\mathbb{R}^n$, the half spaces $\mathbb{R}^n_+$ and the unbounded tube shape domains in $\mathbb{R}^n$. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms. The proof is based on carefully using the moving plane method together with various maximum principles and Hopf's lemmas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_01185 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Unbounded Domains Zhang, Weijun Zhang, Zhitao Analysis of PDEs Functional Analysis In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Ampère systems for instance, considering \begin{equation*} \det(D^2u^i)=f^i(x,{\bf u},\nabla u^i), \ 1\leq i\leq m, \end{equation*} over unbounded domains of various cases, including the whole spaces $\mathbb{R}^n$, the half spaces $\mathbb{R}^n_+$ and the unbounded tube shape domains in $\mathbb{R}^n$. We obtain monotonic and symmetric properties of the solutions to the problem with respect to the geometry of domains and the monotonic and symmetric properties of right-hand side terms. The proof is based on carefully using the moving plane method together with various maximum principles and Hopf's lemmas. |
| title | Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Unbounded Domains |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2404.01185 |