AI 中文总结
本文针对对数拉普拉斯算子，建立Schauder型估计，证明非齐次项为κ阶Hölder连续时内部解的正则性，并给出非负解的Harnack不等式。
AI 中文摘要
本文建立对数拉普拉斯算子的Schauder型估计，证明当非齐次项为κ阶Hölder连续时，内部解也为κ阶Hölder连续，且内部正则性在对数修正下略超κ阶Hölder光滑性，还证明了非负解的Harnack不等式。
英文摘要
In this article, we establish Schauder-type estimates for the logarithmic Laplacian. We show that for a $κ$-Hölder inhomogeneous term, the solution is also $κ$-Hölder in the interior. In fact, the interior regularity slightly exceeds $κ$-Hölder smoothness up to a logarithmic correction. Additionally, we prove a Harnack inequality for non-negative solutions.
Comments22 pages
