Lipschitz regularity for fully nonlinear elliptic equations with $(p,q)$-growth
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913131219910656 |
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| author | Byun, Sun-Sig Kim, Hongsoo |
| author_facet | Byun, Sun-Sig Kim, Hongsoo |
| contents | We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with $(p,q)$-growth. We prove that for a small gap $q-p$, a solution is locally or globally Lipschitz continuous. We also prove that a given Hölder continuous solution is Lipschitz continuous under improved bounds for the gap. These gap conditions are similar to those required for the regularity of double phase problems in divergence form. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_15119 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Lipschitz regularity for fully nonlinear elliptic equations with $(p,q)$-growth Byun, Sun-Sig Kim, Hongsoo Analysis of PDEs 35B65, 35D40, 35J15, 35J25 We prove the interior and global Lipschitz regularity results for a solution of fully nonlinear equations with $(p,q)$-growth. We prove that for a small gap $q-p$, a solution is locally or globally Lipschitz continuous. We also prove that a given Hölder continuous solution is Lipschitz continuous under improved bounds for the gap. These gap conditions are similar to those required for the regularity of double phase problems in divergence form. |
| title | Lipschitz regularity for fully nonlinear elliptic equations with $(p,q)$-growth |
| topic | Analysis of PDEs 35B65, 35D40, 35J15, 35J25 |
| url | https://arxiv.org/abs/2505.15119 |