Second-order boundary estimates for solutions to a class of quasilinear elliptic equations
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918101647360000 |
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| author | Spadaro, Giuseppe Vuono, Domenico |
| author_facet | Spadaro, Giuseppe Vuono, Domenico |
| contents | We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16402 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Second-order boundary estimates for solutions to a class of quasilinear elliptic equations Spadaro, Giuseppe Vuono, Domenico Analysis of PDEs 35B65, 35J25, 35J62 We prove global second-order regularity for a class of quasilinear elliptic equations, both with homogeneous Dirichlet and Neumann boundary conditions. A condition on the integrability of the second fundamental form on the boundary of the domain is required. As a consequence, with the additional assumption that the source term has a sign, we obtain integrability properties of the inverse of the gradient of the solution. Assuming convexity of the domain, no boundary regularity is required. |
| title | Second-order boundary estimates for solutions to a class of quasilinear elliptic equations |
| topic | Analysis of PDEs 35B65, 35J25, 35J62 |
| url | https://arxiv.org/abs/2507.16402 |