Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866917987505668096 |
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| author | Chhetri, Maya Mavinga, Nsoki Pardo, Rosa |
| author_facet | Chhetri, Maya Mavinga, Nsoki Pardo, Rosa |
| contents | We use De Giorgi-Nash-Moser iteration scheme to establish that weak solutions to a coupled system of elliptic equations with critical growth on the boundary are in $L^\infty(Ω)$. Moreover, we provide an explicit $L^\infty(Ω)$- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of $H^1(Ω)$-norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12434 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems Chhetri, Maya Mavinga, Nsoki Pardo, Rosa Analysis of PDEs 35B45, 35J65, 35J61, 35J47 We use De Giorgi-Nash-Moser iteration scheme to establish that weak solutions to a coupled system of elliptic equations with critical growth on the boundary are in $L^\infty(Ω)$. Moreover, we provide an explicit $L^\infty(Ω)$- estimate of weak solutions with subcritical growth on the boundary, in terms of powers of $H^1(Ω)$-norms, by combining the elliptic regularity of weak solutions with Gagliardo--Nirenberg interpolation inequality. |
| title | Regularity and explicit $L^\infty$ estimates for a class of nonlinear elliptic systems |
| topic | Analysis of PDEs 35B45, 35J65, 35J61, 35J47 |
| url | https://arxiv.org/abs/2504.12434 |