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

2021/02/15 by Abja, Soufian, Olive, Guillaume
#32W20 #35J70 #Analysis of PDEs (math.AP) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2102.07553

Abstract

In this paper, we establish a local regularity result for W^2,p_loc solutions to complex degenerate nonlinear elliptic equations F(D²_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.

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