Uniform estimates for elliptic equations with Carathéodory nonlinearities at the interior and on the boundary
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866913709667909632 |
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| author | Antonio, Edgar Árciga-Alejandre, Martín P. Pardo, Rosa Ortiz, Jorge Sánchez |
| author_facet | Antonio, Edgar Árciga-Alejandre, Martín P. Pardo, Rosa Ortiz, Jorge Sánchez |
| contents | We establish an explicit uniform a priori estimate for weak solutions to slightly subcritical elliptic problems with nonlinearities simultaneously at the interior and on the boundary. Our explicit $L^{\infty}(Ω)$ a priori estimates are in terms of powers of their $H^{1}(Ω)$ norms. To prove our result, we combine a De Giorgi-Nash-Moser's iteration scheme together with elliptic regularity and the Gagliardo-Nirenberg's interpolation inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14609 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform estimates for elliptic equations with Carathéodory nonlinearities at the interior and on the boundary Antonio, Edgar Árciga-Alejandre, Martín P. Pardo, Rosa Ortiz, Jorge Sánchez Analysis of PDEs 35B45, 35B66, 35B33, 35J75, 35J25 We establish an explicit uniform a priori estimate for weak solutions to slightly subcritical elliptic problems with nonlinearities simultaneously at the interior and on the boundary. Our explicit $L^{\infty}(Ω)$ a priori estimates are in terms of powers of their $H^{1}(Ω)$ norms. To prove our result, we combine a De Giorgi-Nash-Moser's iteration scheme together with elliptic regularity and the Gagliardo-Nirenberg's interpolation inequality. |
| title | Uniform estimates for elliptic equations with Carathéodory nonlinearities at the interior and on the boundary |
| topic | Analysis of PDEs 35B45, 35B66, 35B33, 35J75, 35J25 |
| url | https://arxiv.org/abs/2502.14609 |