论文标题
Hörmander类型运营商的弱解决方案的Hölder规律性
Hölder regularity for weak solutions of Hörmander type operators
论文作者
论文摘要
在最新的（可能有条件的）规律性的结果中，我们证明了Poincaré不平等的抛物线版本，因此，我们以关键的方式推断出古典Moser迭代技术的版本。这一贡献的目的是强调，即使在{\ sl parerabolic}设置中，也可以以缺乏统一性的价格使用Moser参数的{\ sl椭圆形}版本。然而，这足以推断出弱解决方案的规律性。证明是基本的，自然而然地统一了有关kolmogorov方程，下层及其某些变化的文献中的几个结果。
Motivated by recent results on the (possibly conditional) regularity for time-dependent hypoelliptic equations, we prove a parabolic version of the Poincaré inequality, and as a consequence, we deduce a version of the classical Moser iteration technique using in a crucial way the geometry of the equation. The point of this contribution is to emphasize that one can use the {\sl elliptic} version of the Moser argument at the price of the lack of uniformity, even in the {\sl parabolic } setting. This is nevertheless enough to deduce Hölder regularity of weak solutions. The proof is elementary and unifies in a natural way several results in the literature on Kolmogorov equations, subelliptic ones and some of their variations.
