Lipschitz regularity for anisotropic fully nonlinear equations with nonstandard growth
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915376964567040 |
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| author | Byun, Sun-Sig Kim, Hongsoo |
| author_facet | Byun, Sun-Sig Kim, Hongsoo |
| contents | We establish interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, without imposing any restriction on the gap between the highest and lowest growth exponents. Our proof is based on an anisotropic variant of the seminal Ishii Lions method. Our result furnishes a viscosity analogue of the divergence-form theory in [Bousquet20], adapted to the non-divergence setting. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for anisotropic fully nonlinear equations with nonstandard growth Byun, Sun-Sig Kim, Hongsoo Analysis of PDEs 35B65, 35D40, 35J15, 35J25, 35J70 We establish interior Lipschitz regularity for solutions to anisotropic fully nonlinear equations with nonstandard growth, without imposing any restriction on the gap between the highest and lowest growth exponents. Our proof is based on an anisotropic variant of the seminal Ishii Lions method. Our result furnishes a viscosity analogue of the divergence-form theory in [Bousquet20], adapted to the non-divergence setting. |
| title | Lipschitz regularity for anisotropic fully nonlinear equations with nonstandard growth |
| topic | Analysis of PDEs 35B65, 35D40, 35J15, 35J25, 35J70 |
| url | https://arxiv.org/abs/2507.05712 |