偶数阶椭圆方程组的临界正则性与紧性理论——献给李工宝教授 70 寿辰

Abstract

Abstract:

We deduce optimal higher order regularity result for the even order geometrical elliptic system

$\begin{equation*} \Delta^{k}u=\sum_{l=0}^{k-1}\Delta^{l}\left\langle V_{l},{\rm d}u\right\rangle +\sum_{l=0}^{k-2}\Delta^{l}\delta\left(w_{l}{\rm d}u\right)+f \quad \text{in } B_1 \subset\mathbb{R}^m,\end{equation*}$

where all the coefficients $ \{V_l, w_l\}_{l} $ are assumed to have the smallnest regularity and $ f $ lies in the borderline function space $ L\log L(B_1) $. As an application, we also obtain a compactness result.

Key words: even order elliptic system, regularity, compactness, decay estimate

CLC Number:

O175.25

Changlin Xiang, Jie Wang, Binhang Zhang, Yanping Zhou. Borderline Regularity and Compactness Theory for An Even Order Elliptic Systems[J].Acta mathematica scientia,Series A, 2025, 45(6): 1806-1813.

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References 22

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Borderline Regularity and Compactness Theory for An Even Order Elliptic Systems

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