12 citations · 19 across the 7 of their papers we have counts for
5 papers · 1 filter
Asymptotic expansion of the annealed Green's function and its derivatives
Matthias Keller, Marius Lemm
We consider random elliptic equations in dimension at small ellipticity contrast. We derive the large-distance asymptotic expansion of the annealed Green's function up to…
Optimal Hardy weights on the Euclidean lattice
Matthias Keller, Marius Lemm
We investigate the large-distance asymptotics of optimal Hardy weights on , , via the super solution construction. For the free discrete Laplacian, the Hardy…
A remark on a surprising result by Bourgain in homogenization
Mitia Duerinckx, Antoine Gloria, Marius Lemm
In a recent work, Bourgain gave a fine description of the expectation of solutions of discrete linear elliptic equations on with random coefficients in a perturbative…
On the averaged Green's function of an elliptic equation with random coefficients
Jongchon Kim, Marius Lemm
We consider a divergence-form elliptic difference operator on the lattice , with a coefficient matrix that is an i.i.d. perturbation of the identity matrix. Recently,…
On the Hölder regularity for the fractional Schrödinger equation and its improvement for radial data
Marius Lemm
We consider the linear, time-independent fractional Schrödinger equation We are interested in the local Hölder exponents of distributional solutions , assum…