Regularity theory for fully nonlinear equations of porous medium-type
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910545684201472 |
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| author | Yun, Hyungsung |
| author_facet | Yun, Hyungsung |
| contents | In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global $C^{2,α}$-estimates of viscosity solutions. In many PDE problems, the $C^{2,α}$-estimates have been obtained through Schauder-type estimates. However, the Schauder-type estimates are not applicable to the porous medium-type equations. We provide techniques for handling porous medium-type equations so that the global $C^{2,α}$-estimates can be established. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20022 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Regularity theory for fully nonlinear equations of porous medium-type Yun, Hyungsung Analysis of PDEs Primary 35B65, Secondary 35D40, 35K55, 35K65 In this paper, we establish the regularity results for nonnegative viscosity solutions to fully nonlinear equations of porous medium-type in bounded domains with the zero Dirichlet boundary condition, to be precise, we prove the global $C^{2,α}$-estimates of viscosity solutions. In many PDE problems, the $C^{2,α}$-estimates have been obtained through Schauder-type estimates. However, the Schauder-type estimates are not applicable to the porous medium-type equations. We provide techniques for handling porous medium-type equations so that the global $C^{2,α}$-estimates can be established. |
| title | Regularity theory for fully nonlinear equations of porous medium-type |
| topic | Analysis of PDEs Primary 35B65, Secondary 35D40, 35K55, 35K65 |
| url | https://arxiv.org/abs/2407.20022 |