An elliptic Harnack inequality for difference equations with random balanced coefficients
An elliptic Harnack inequality for difference equations with random balanced coefficients
复制标题
具有随机平衡系数的差分方程的椭圆 Harnack 不等式
作者：
Noam Berger;Moran Cohen;J. Deuschel;Xiaoqin Guo
对于具有平衡独立同分布的差分方程的非负解，证明了格Z上大规模椭圆Harnack不等式不一定是椭圆的系数。我们还确定了Harnack不等式中的最佳常数。我们的证明依赖于相应的不变性原理布朗运动的定量均匀化结果，并在渗流估计。作为我们的主要定理的推论，我们得到一个几乎最优的Hölder估计。
We prove an elliptic Harnack inequality at large scale on the lattice Z, for non-negative solutions of a difference equation with balanced i.i.d. coefficients which are not necessarily elliptic. We also identify the optimal constant in the Harnack inequality. Our proof relies on a quantitative homogenization result of the corresponding invariance principle to Brownian motion, and on percolation estimates. As a corollary of our main theorem we derive an almost optimal Hölder estimate.
影响因子：
1.4
作者：
Guo, Xiaoqin;Peterson, Jonathon;Tran, Hung V.
通讯作者：
Tran, Hung V.
具有时间相关遍历简并权重的随机游走的淬火不变性原理
DOI：
10.1214/17-aop1186
发表时间：
2018
期刊：
arXiv: Probability
影响因子：
--
作者：
S. Andres;A. Chiarini;J.-D. Deuschel;M. Slowik
通讯作者：
M. Slowik