Weighted estimates for Hodge-Maxwell systems
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915762325684224 |
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| author | Mahato, Rohit Sil, Swarnendu |
| author_facet | Mahato, Rohit Sil, Swarnendu |
| contents | We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems
\begin{align*}
d^{\ast}\left(Adω\right) + B^{\intercal}dd^{\ast}\left(Bω\right) = λBω+ f \quad \text{ in } Ω
\end{align*}
with either $ν\wedge ω$ and $ν\wedge d^{\ast}\left(Bω\right)$ or $ν\lrcorner Bω$ and $ν\lrcorner Adω$ prescribed on $\partialΩ.$ As a consequence, we prove the solvability of Hodge-Maxwell systems and derive Hodge decomposition theorems in weighted Lebesgue spaces. Our proof avoids potential theory, does not rely on representation formulas and instead uses decay estimates in the spirit of `Campanato method' to establish weighted $L^{p}$ estimates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22604 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Weighted estimates for Hodge-Maxwell systems Mahato, Rohit Sil, Swarnendu Analysis of PDEs 35B65, 35J56, 35J57, 35Q61, 35B45 We establish up to the boundary regularity estimates in weighted $L^{p}$ spaces with Muckenhoupt weights $A_{p}$ for weak solutions to the Hodge systems \begin{align*} d^{\ast}\left(Adω\right) + B^{\intercal}dd^{\ast}\left(Bω\right) = λBω+ f \quad \text{ in } Ω \end{align*} with either $ν\wedge ω$ and $ν\wedge d^{\ast}\left(Bω\right)$ or $ν\lrcorner Bω$ and $ν\lrcorner Adω$ prescribed on $\partialΩ.$ As a consequence, we prove the solvability of Hodge-Maxwell systems and derive Hodge decomposition theorems in weighted Lebesgue spaces. Our proof avoids potential theory, does not rely on representation formulas and instead uses decay estimates in the spirit of `Campanato method' to establish weighted $L^{p}$ estimates. |
| title | Weighted estimates for Hodge-Maxwell systems |
| topic | Analysis of PDEs 35B65, 35J56, 35J57, 35Q61, 35B45 |
| url | https://arxiv.org/abs/2601.22604 |