Center for Nonlinear Analysis
CNA Home
People
Seminars
Publications
Workshops and Conferences
CNA Working Groups
CNA Comments Form
Summer Schools
Summer Undergraduate Institute
PIRE
Cooperation
Graduate Topics Courses
SIAM Chapter Seminar
Positions
Contact |
CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Xiaoqin Guo UW Madison Title: Quantitative homogenization and Harnack inequality for a non-elliptic balanced random environment Abstract: In the d-dimensional integer lattice $\mathbb Z^d$, $d\ge 2$, we consider a discrete non-divergence form difference operator $$ L_a u(x)=\sum_{i=1}^d a_i(x)[u(x+e_i)+u(x-e_i)-2u(x)] $$ where $a(x)=diag(a_1(x),..., a_d(x)), x\in\mathbb Z^d$ are random nonnegative diagonal matrices which are independent and identically distributed. A difficulty in studying this problem is that eigenvalues of $a(x)$ are allowed to be zero. In this talk, using random walks in random media and its percolative structure, we present a Harnack inequality and quantitative homogenization result for this random operator. Joint work with N.Berger, M.Cohen and J.-D. Deuschel.Recording: http://mm.math.cmu.edu/recordings/cna/xiaoqin_guo_small.mp4Date: Tuesday, March 27, 2018Time: 1:30 pmLocation: Wean Hall 7218Submitted by: Ian Tice |