Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Soufian Abja (1) , Guillaume Olive (1)

1 Faculty of Mathematics and Computer Science of the Jagiellonian University

In this paper, we establish a local regularity result for $W^{2,p}_{\mathrm{loc}}$ solutions to complex degenerate nonlinear elliptic equations $F(D^2_{\mathbb{C}} u)=f$ when they are comparable to the Monge-Ampère equation. Notably, we apply our result to the so-called $k$-Monge-Ampère equation.

Mots clés: degenerate elliptic equations; local regularity; Hessian equations

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

Soufian Abja, Guillaume Olive. Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation. 2021. ⟨hal-03141740⟩