动态理论中的定量德乔基方法

Journal de l’École polytechnique — Mathématiques Pub Date : 2021-03-17 DOI:10.5802/jep.203

Jessica Guerand, C. Mouhot

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引用次数: 23

摘要

我们考虑在漂移-扩散算子中具有粗糙系数的动力学Fokker-Planck型准椭圆方程，也称为Kolmogorov或超抛物线方程。给出了De Giorgi中值引理以及弱哈纳克不等式和哈纳克不等式的简短定量证明。这意味着H{\ ' o}与定量估计的更大连续性。这张纸是独立的。

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Quantitative De Giorgi methods in kinetic theory

We consider hypoelliptic equations of kinetic Fokker-Planck type, also known as Kolmogorov or ultraparabolic equations, with rough coefficients in the drift-diffusion operator. We give novel short quantitative proofs of the De Giorgi intermediate-value Lemma as well as weak Harnack and Harnack inequalities. This implies H{\"o}lder continuity with quantitative estimates. The paper is self-contained.

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Journal de l’École polytechnique — Mathématiques

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