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

2021/02/15 by Soufian Abja, Abja, Soufian, Guillaume Olive +1
Mathematics · #32W20 #35J70 #Analysis of PDEs (math.AP) #Combinatorics #Complex Variables (math.CV) #Degenerate energy levels #Elliptic curve #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Homogeneous #Mathematical analysis #Mathematical physics #Mathematics #Monge–Ampère equation #Nonlinear Partial Differential Equations #Nonlinear system #Physics #Pure mathematics #Quantum mechanics #math.AP #math.CV #msc:32W20 #msc:35J70

paper · pdf · doi:10.48550/arxiv.2102.07553

published in arXiv (Cornell University) (Cornell University) · Comments are always welcome

arxiv created 2021/02/15 · openalex publication_date 2021/02/15 · arxiv updated 2021/02/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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