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

Abstract

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

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