论文标题
Moser对Harnack不平等的证明的轨迹解释
A trajectorial interpretation of Moser's proof of the Harnack inequality
论文作者
论文摘要
1971年，Moser出版了他的简化版本，证明了抛物线Harnack不平等现象。核心的新成分是由于Bombieri和Giusti而导致的基本引理，它结合了$ l^p-l^\ infty $ esstimate和弱的$ l^1 $ estimate，以实现超弹的对数。在本说明中，我们给出了这个弱的$ l^1 $ estimate的新颖证明。提出的论点使用抛物线轨迹，不使用任何庞加莱不平等。此外，提出的论点对Moser的结果提供了几何解释，并可以使Moser的方法转移到其他方程式。
In 1971 Moser published a simplified version of his proof of the parabolic Harnack inequality. The core new ingredient is a fundamental lemma due to Bombieri and Giusti, which combines an $L^p-L^\infty$-estimate with a weak $L^1$-estimate for the logarithm of supersolutions. In this note, we give a novel proof of this weak $L^1$-estimate. The presented argument uses parabolic trajectories and does not use any Poincaré inequality. Moreover, the proposed argument gives a geometric interpretation of Moser's result and could allow transferring Moser's method to other equations.
