论文标题
关于抛物线派的言论
Remarks on parabolic De Giorgi classes
论文作者
论文摘要
我们对抛物线de Giorgi类中的功能属性的属性$ p $发表了几篇评论。有一些新的观点，包括一种新型的衡量阳性，凸组成下的成员资格的繁殖机制以及对数类型的估计。基于它们，我们能够提供已知属性的新证明。特别是，我们通过Moser的思想证明了这些功能的本地界限和本地Hölder连续性，从而避免了De Giorgi的重型机械。我们还抓住了这个机会，为某些超级级别的de Giorgi的非负成员提供了透明的证据，证明了harnack不平等的不平等，而没有任何涵盖的论点。
We make several remarks concerning properties of functions in parabolic De Giorgi classes of order $p$. There are new perspectives including a novel mechanism of propagating positivity in measure, the reservation of membership under convex composition, and a logarithmic type estimate. Based on them, we are able to give new proofs of known properties. In particular, we prove local boundedness and local Hölder continuity of these functions via Moser's ideas, thus avoiding De Giorgi's heavy machinery. We also seize this opportunity to give a transparent proof of a weak Harnack inequality for non-negative members of some super-class of De Giorgi, without any covering argument.
