论文标题
通过harnack方法和对非线性椭圆形问题的应用进行翻转规律性
Flipping regularity via the Harnack approach and applications to nonlinear elliptic problems
论文作者
论文摘要
我们证明了一个抽象的结果，以确保单方面的几何控制得出满足一般条件的功能的双向估计。我们的发现在非线性椭圆问题的背景下引起了共鸣，包括对完全非线性椭圆方程的超溶液和de Giorgi类中的功能。抽象结果的后果之一是规律性估计，以及在粘度解决方案类别中连续函数的条件。我们还证明，单方面的几何控制产生$ l^pl^\ infty $估计。它与de giorgi-nash-moser理论中的含义相反。
We prove an abstract result ensuring that one-sided geometric control yields two-sided estimates for functions satisfying general conditions. Our findings resonate in the context of nonlinear elliptic problems, including supersolutions to fully nonlinear elliptic equations and functions in the De Giorgi class. Among the consequences of our abstract results are regularity estimates, and conditions for a continuous function to be in the class of viscosity solutions. We also prove that one-sided geometric control yields $L^pL^\infty$-estimates. It provides a converse to the implication in the De Giorgi-Nash-Moser theory.
