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De Giorgi–Nash–Moser theory under coarse ellipticity

Scott Armstrong, Benny Avelin, Tuomo Kuusi, Aatu Turpeinen

Palomar Registrypalomar/PALOMAR-2026-10-11-000003Oct 11, 2026math.APscore 0

A Lean 4 formalization of the paper "Coarse ellipticity and De Giorgi–Nash–Moser theory in the optimal range" by S. Armstrong, B. Avelin, T. Kuusi and A. Turpeinen (arXiv:2610.11879). The paper extends the theory of De Giorgi–Nash–Moser to elliptic equations with symmetric coefficients a(x) which are possibly degenerate and unbounded but satisfy a coarse ellipticity condition: spatial moments of coarse-grained matrices, suitably discounted and summed across scales, are finite. Under this condition it proves local upper bounds for weak subsolutions, a weak Harnack inequality for nonnegative…

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