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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…
math.AP2025
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…