发表机构
Laboratoire de Mathématiques de Versailles, UMR 8100 CNRS, UVSQ, Université Paris-Saclay（凡尔赛数学实验室，CNRS联合研究单位8100，凡尔赛大学，巴黎萨克雷大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对退化非局部方程，通过Harnack型不等式证明瞬时平滑效应，移除先前非退化假设，并用Bombieri-Giusti方法获得定量估计。
AI 中文摘要
我们证明了一个退化非局部演化方程（最初作为活性布朗粒子系统的多粒子极限推导而来）的瞬时平滑效应。其潜在机制是，通过推导一个平均量的Harnack型不等式，我们能够证明该方程在正时间内变为强抛物型，从而具有自正则化性质。本文是对先前工作的显著改进，先前工作对初始数据施加了额外的（弱）非退化假设。在此，我们完全移除这些假设，并通过Bombieri-Giusti方法证明（除正则性自举外）上述平均量的定量估计。
英文摘要
We prove an instantaneous smoothing effect for a degenerate non-local evolution equation (originally derived as the many-particle limit of a system of active Brownian particles). The underlying mechanism is that, by deriving a Harnack-type inequality for an averaged quantity, we are able to show that the equation becomes strongly parabolic for positive times, and thus self-regularising. This paper is a significant improvement of a previous work, where additional (weak) non-degeneracy assumptions were imposed on the initial data. Herein, we completely remove these assumptions, and prove (in addition to the regularity bootstrap) quantitative estimates on the aforementioned averaged quantity by means of an approach à la Bombieri-Giusti.
Comments40 pages
