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Talk

A Liouville property for the random conductance model

  • Tuan Anh Nguyen (Universität Duisburg-Essen)
G3 10 (Lecture hall)

Abstract

In the talk, I will give an introduction to my research based on a work by Bella, Fehrman, and Otto on stochastic homogenization. Consider the random differential operator $\nabla\cdot a\nabla $ where the random matrix (coefficient field) $a$ is assumed to be stationary and ergodic. By making use of the extended correctors $(\phi,\sigma)$ and choosing a reasonable homogenization error, they can obtain a regularity estimate, namely the excess decay, which implies a Liouville principle for $a$-harmonic functions, i.e. functions satisfying $\nabla \cdot a \nabla u=0$. It is interesting to know whether their ideas work in the discrete case (the random conductance model on the lattice). The answer is positive: By using several analytic and numerical methods, it is possible to implement their ideas in the discrete case.

Katja Heid

MPI for Mathematics in the Sciences Contact via Mail

Upcoming Events of This Seminar

  • Mar 11, 2024 tba with Carlos Román Parra
  • Mar 15, 2024 tba with Esther Bou Dagher