359 citations · 1k across the 39 of their papers we have counts for
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Homogenization at a polynomial scale in high contrast
Scott Armstrong, Tuomo Kuusi, Amélie Loher
We prove an upper bound on the homogenization length scale which is a fixed power of the coarse ellipticity ratio for coefficient fields that satisfy a finite range of dependence a…
Coarse-grained ellipticity and De Giorgi-Nash-Moser theory
Scott Armstrong, Benny Avelin, Cristiana De Filippis +2
We prove local boundedness and a Harnack inequality for nonnegative weak solutions of the equation under a coarse-grained ellipticity assump…
A coarse-graining theory for elliptic operators and homogenization in high contrast
Scott Armstrong, Tuomo Kuusi
We review a coarse-graining theory for divergence-form elliptic operators. The construction centers on a pair of coarse-grained matrices defined on spatial blocks that encode a sca…
Gradient regularity and first-order potential estimates for a class of nonlocal equations
Tuomo Kuusi, Simon Nowak, Yannick Sire
We consider nonlocal equations of order larger than one with measure data and prove gradient regularity in Sobolev and Hölder spaces as well as pointwise bounds of the gradient in…
Elliptic homogenization from qualitative to quantitative
Scott Armstrong, Tuomo Kuusi
We give a self-contained introduction to the theory of elliptic homogenization for random coefficient fields, starting from classical qualitative homogenization. The presentation a…
Quantitative homogenization for the obstacle problem and its free boundary
Gohar Aleksanyan, Tuomo Kuusi
In this manuscript we prove quantitative homogenization results for the obstacle problem with bounded measurable coefficients. As a consequence, large-scale regularity results both…