Hessian estimates for Lagrangian mean curvature equation with Lipschitz critical and supercritical phases
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_ | 1866909393663033344 |
|---|---|
| author | Ding, Qi |
| author_facet | Ding, Qi |
| contents | In this paper, we develop a new strategy to study Lagrangain mean curvature equation on open sets of $\mathbb{R}^{n}(n\geq2)$. By establishing an Allard-type regularity theorem, we obtain an interior Hessian estimate of solutions to this equation with prescribed Lipschitz critical and supercritical phases. Here, our condition on the phases is sharp. The proof heavily relies on geometric measure theory, geometry of Lagrangian graphs, and De Giorgi-Nash-Moser iteration. We expect that the techniques and ideas developed here can be used in some other equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07511 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hessian estimates for Lagrangian mean curvature equation with Lipschitz critical and supercritical phases Ding, Qi Differential Geometry Analysis of PDEs In this paper, we develop a new strategy to study Lagrangain mean curvature equation on open sets of $\mathbb{R}^{n}(n\geq2)$. By establishing an Allard-type regularity theorem, we obtain an interior Hessian estimate of solutions to this equation with prescribed Lipschitz critical and supercritical phases. Here, our condition on the phases is sharp. The proof heavily relies on geometric measure theory, geometry of Lagrangian graphs, and De Giorgi-Nash-Moser iteration. We expect that the techniques and ideas developed here can be used in some other equations. |
| title | Hessian estimates for Lagrangian mean curvature equation with Lipschitz critical and supercritical phases |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2411.07511 |