Estimates on elliptic equations that hold only where the gradient is large

Cyril Imbert (1) , Luis Silvestre (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 Department of Mathematics [Chicago]

We consider a function which is a viscosity solution of a uniformly elliptic equation only at those points where the gradient is large. We prove that the Hölder estimates and the Harnack inequality, as in the theory of Krylov and Safonov, apply to these functions.

Mots clés: Degenerate elliptic equations; regularity; viscosity solutions

Domaines: Equations aux dérivées partielles [math.AP]

Cyril Imbert, Luis Silvestre. Estimates on elliptic equations that hold only where the gradient is large. Journal of the European Mathematical Society, 2016, 18, pp.1321-1338. ⟨10.4171/JEMS/614⟩. ⟨hal-00832550v3⟩