Schauder--Orlicz-Type Estimates for Divergence-Form Elliptic Equations with Lower-Order Terms
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866914596488478720 |
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| author | Bourabiaa, Jaouad Elmadani, Youssef Hanine, Abdelouahab |
| author_facet | Bourabiaa, Jaouad Elmadani, Youssef Hanine, Abdelouahab |
| contents | Schauder Orlicz-type estimates are derived for weak solutions to second-order linear elliptic equations in divergence form with lower-order terms. The Orlicz setting $X=L^ψ$ is treated first. Under suitable assumptions on the Young function $ψ$ and on the coefficients, the optimal associated space for the lower-order datum is identified. An \textit{a priori} estimate in $W^{1,ψ}$ is then obtained. The discussion is next extended to rearrangement-invariant Banach function spaces. A class $(\mathcal C)$ is introduced to characterize the spaces $X$ for which a corresponding associated space $Y$ yields Schauder-type estimates. Lorentz spaces are finally examined as concrete examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24596 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schauder--Orlicz-Type Estimates for Divergence-Form Elliptic Equations with Lower-Order Terms Bourabiaa, Jaouad Elmadani, Youssef Hanine, Abdelouahab Analysis of PDEs 35B45, 35J25, 46E30 Schauder Orlicz-type estimates are derived for weak solutions to second-order linear elliptic equations in divergence form with lower-order terms. The Orlicz setting $X=L^ψ$ is treated first. Under suitable assumptions on the Young function $ψ$ and on the coefficients, the optimal associated space for the lower-order datum is identified. An \textit{a priori} estimate in $W^{1,ψ}$ is then obtained. The discussion is next extended to rearrangement-invariant Banach function spaces. A class $(\mathcal C)$ is introduced to characterize the spaces $X$ for which a corresponding associated space $Y$ yields Schauder-type estimates. Lorentz spaces are finally examined as concrete examples. |
| title | Schauder--Orlicz-Type Estimates for Divergence-Form Elliptic Equations with Lower-Order Terms |
| topic | Analysis of PDEs 35B45, 35J25, 46E30 |
| url | https://arxiv.org/abs/2605.24596 |