4 papers · 1 filter
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…
Formalization of De Giorgi--Nash--Moser Theory in Lean
Scott Armstrong, Julia Kempe
We present a formalization in Lean of the core interior De Giorgi--Nash--Moser theory for uniformly elliptic divergence-form equations with bounded measurable coefficients. The for…
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…