Quasi-Harnack inequality
Quasi-Harnack inequality
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拟哈纳克不等式
DOI：
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发表时间：
2018
影响因子：
1.7
通讯作者：
O. Savin
中科院分区：
文献类型：
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作者：
D. Silva;O. Savin
摘要：本文得到了经典的Krylov-Safonov Harnack不等式的一些推广。新奇之处在于，我们考虑的函数不一定满足无穷小方程，而是表现出两个尺度的行为。我们要求当尺度大于$r0>；0$(小)时，函数满足标准二次多项式族的比较原理，而在尺度$r0$时，满足弱Harnack型估计。我们还给出了主要结果在离散差分方程、非局部方程、齐次化和Almgren拟极小曲面上的一些应用。
abstract:In this paper we obtain some extensions of the classical Krylov-Safonov Harnack inequality. The novelty is that we consider functions that do not necessarily satisfy an infinitesimal equation but rather exhibit a two-scale behavior. We require that at scale larger than some $r_0>0$ (small) the functions satisfy the comparison principle with a standard family of quadratic polynomials, while at scale $r_0$ they satisfy a Weak Harnack type estimate.We also give several applications of the main result in very different settings such as discrete difference equations, nonlocal equations, homogenization and the quasi-minimal surfaces of Almgren.