Fine boundary regularity for fully nonlinear mixed local-nonlocal problems
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866914024524873728 |
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| author | Modasiya, Mitesh Sen, Abhrojyoti |
| author_facet | Modasiya, Mitesh Sen, Abhrojyoti |
| contents | We consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. For a bounded $C^2$ domain $Ω\subset \mathbb{R}^d,$ let $u\in C(\mathbb{R}^d)$ be a viscosity solution of such Dirichlet problem. We obtain global Lipschitz regularity and fine boundary regularity for $u$ by constructing appropriate sub and supersolutions coupled with a Harnack type inequality. We apply these results to obtain Hölder regularity of $Du$ up to the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02397 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fine boundary regularity for fully nonlinear mixed local-nonlocal problems Modasiya, Mitesh Sen, Abhrojyoti Analysis of PDEs 35D40, 47G20, 35J60, 35B65 We consider Dirichlet problems for fully nonlinear mixed local-nonlocal non-translation invariant operators. For a bounded $C^2$ domain $Ω\subset \mathbb{R}^d,$ let $u\in C(\mathbb{R}^d)$ be a viscosity solution of such Dirichlet problem. We obtain global Lipschitz regularity and fine boundary regularity for $u$ by constructing appropriate sub and supersolutions coupled with a Harnack type inequality. We apply these results to obtain Hölder regularity of $Du$ up to the boundary. |
| title | Fine boundary regularity for fully nonlinear mixed local-nonlocal problems |
| topic | Analysis of PDEs 35D40, 47G20, 35J60, 35B65 |
| url | https://arxiv.org/abs/2301.02397 |