Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2021

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 $W^{2,p}_{\mathrm{loc}}$ 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.
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Dates and versions

hal-03141740 , version 1 (15-02-2021)

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  • HAL Id : hal-03141740 , version 1

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

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