Orateur
Théo Lavier
Description
We present work in progress on quantitative homogenization results for viscosity solutions of $\infty$-Laplacian-type equations of the form$$\nabla\!\left(a\!\left(\tfrac{\cdot}{\varepsilon}\right)\vert{}\nabla u_\varepsilon\vert{}^2\right)\cdot \nabla u_\varepsilon = 0,$$subject to Dirichlet boundary conditions in dimensions $d\leq 3$, where the coefficient field $a : \mathbb{R}^d\rightarrow \mathbb{R}$ is random and sampled from a stationary, ergodic, and isotropic probability measure. We approach this problem using a quantitative power-law approximation of the solution $u_\varepsilon$, combined with quantitative homogenization results for nonlinear elliptic equations with $p$-growth for $p>2$.