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arXiv · 2102.07553

Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Amp\`ere equation

Soufian Abja·Guillaume Olive
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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-Amp\`ere equation. Notably, we apply our result to the so-called $k$-Monge-Amp\`ere equation.

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Soufian Abja, Guillaume Olive. 2021-02-15. Local regularity for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Amp\`ere equation. https://doi.org/10.1007/s10231-021-01129-y

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