Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja (1) , Sławomir Dinew (1) , Guillaume Olive (1)

1 Institute of Mathematics [Krakow]

We prove sharp uniform estimates for strong supersolutions of a large class of fully nonlinear degenerate elliptic complex equations. Our findings rely on ideas of Kuo and Trudinger who dealt with degenerate linear equations in the real setting. We also exploit the pluripotential theory for the complex Monge-Ampère operator as well as suitably tailored theory of $L^p$-viscosity subsolutions.

Mots clés: nonlinear degenerate elliptic equations; viscosity solutions; a priori estimates

Domaines: Equations aux dérivées partielles [math.AP]; Variables complexes [math.CV]

Soufian Abja, Sławomir Dinew, Guillaume Olive. Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation. 2020. ⟨hal-02973743v2⟩