An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917662700863488 |
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| author | Chhetri, Maya Mavinga, Nsoki Pardo, Rosa |
| author_facet | Chhetri, Maya Mavinga, Nsoki Pardo, Rosa |
| contents | We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06304 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary Chhetri, Maya Mavinga, Nsoki Pardo, Rosa Analysis of PDEs 35B45, 35J65, 35J61, 35J15 We establish an explicit $L^\infty(\Om)$ a priori estimate for weak solutions to subcritical elliptic problems with nonlinearity on the boundary, in terms of the powers of their $H^1(\Om)$ norms. To prove our result, we combine in a novel way Moser type estimates together with elliptic regularity and Gagliardo--Nirenberg interpolation inequality. We illustrate our result with an application to subcritical problems satisfying Ambrosetti-Rabinowitz condition. |
| title | An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary |
| topic | Analysis of PDEs 35B45, 35J65, 35J61, 35J15 |
| url | https://arxiv.org/abs/2405.06304 |