Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2020
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866914231189766144 |
|---|---|
| author | Lian, Yuanyuan Wang, Lihe Zhang, Kai |
| author_facet | Lian, Yuanyuan Wang, Lihe Zhang, Kai |
| contents | In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms. In particular, the equations with quadratic growth (called natural growth) in the gradient are covered. We obtain a series of interior and boundary pointwise $C^{k,α}$ regularity ($k\geq 1$ and $0<α<1$). In addition, we also derive the pointwise $C^k$ regularity ($k\geq 1$) and $C^{k,\mathrm{lnL}}$ regularity ($k\geq 0$), which correspond to the end points $α=0$ and $α=1$ respectively. Some regularity results are new even for the linear equations. Moreover, the minimum requirements are imposed to obtain above regularity and our proofs are simple. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2012_00324 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms Lian, Yuanyuan Wang, Lihe Zhang, Kai Analysis of PDEs 35B65, 35D40, 35J60, 35J25 In this paper, we develop systematically the pointwise regularity for viscosity solutions of fully nonlinear elliptic equations in general forms. In particular, the equations with quadratic growth (called natural growth) in the gradient are covered. We obtain a series of interior and boundary pointwise $C^{k,α}$ regularity ($k\geq 1$ and $0<α<1$). In addition, we also derive the pointwise $C^k$ regularity ($k\geq 1$) and $C^{k,\mathrm{lnL}}$ regularity ($k\geq 0$), which correspond to the end points $α=0$ and $α=1$ respectively. Some regularity results are new even for the linear equations. Moreover, the minimum requirements are imposed to obtain above regularity and our proofs are simple. |
| title | Pointwise Regularity for Fully Nonlinear Elliptic Equations in General Forms |
| topic | Analysis of PDEs 35B65, 35D40, 35J60, 35J25 |
| url | https://arxiv.org/abs/2012.00324 |