论文标题
非本地算子的动力学理论中的定量de giorgi方法
Quantitative De Giorgi methods in kinetic theory for non-local operators
论文作者
论文摘要
我们定量地得出了动力学差异方程的harnack不平等现象。这意味着Hölder的连续性。我们的方法基于轨迹，并利用由于能量估计中的非局部性而产生的术语。这允许定量证明非本地性参数$ s \ in（0，1）$的中间值引理。我们的结果从Imbert和Silvestre [22]中恢复了非均匀玻尔兹曼方程的结果。该论文是独立的。
We derive quantitatively the Harnack inequalities for kinetic integro-differential equations. This implies Hölder continuity. Our method is based on trajectories and exploits a term arising due to the non-locality in the energy estimate. This permits to quantitatively prove the intermediate value lemma for the full range of non-locality parameter $s \in (0, 1)$. Our results recover the results from Imbert and Silvestre [22] for the inhomogeneous Boltzmann equation in the non-cutoff case. The paper is self-contained.
