Abstract: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 $X=L^\psi$ is treated first. Under suitable assumptions on the Young function $\psi$ and on the coefficients, the optimal associated space for the lower-order datum is identified. An \textit{a priori} estimate in $W^{1,\psi}$ 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.
| Subjects: | Analysis of PDEs (math.AP) |
| MSC classes: | 35B45, 35J25, 46E30 |
| Cite as: | arXiv:2605.24596 [math.AP] |
| (or arXiv:2605.24596v1 [math.AP] for this version) | |
| https://doi.org/10.48550/arXiv.2605.24596 arXiv-issued DOI via DataCite (pending registration) |
From: Youssef Elmadani [view email]
[v1]
Sat, 23 May 2026 14:21:17 UTC (21 KB)
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