Discrete Green's functions and optimal Hardy weights

15.06.2023 16:15 – 18:15

"We consider elliptic, divergence-form operators on Z^d with random coefficients. Building on a novel perturbative approach to homogenization theory due to Bourgain and subsequent refinements, we derive an asymptotic expansion of the annealed (=averaged) Green’s function and its first (d+1) derivatives at large distances. As a corollary, we show that derivatives up to order d+1 behave like those of the standard Laplacian. In the second part of the talk, we discuss how Green’s function estimates from homogenization theory can be used to estimate Hardy weights. We find that, after suitable averaging, the optimal Hardy weight has the familiar inverse-square behavior at large distances." Joint work with Matthias Keller

Lieu

Bâtiment: Conseil Général 7-9

Room 1-15, Séminaire "Analysis Seminar"

entrée libre