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math.AP2026
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…
math.AP2026
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…
math.AP2026
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…