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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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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03141740
Contributor : Guillaume Olive Connect in order to contact the contributor
Submitted on : Monday, February 15, 2021 - 2:54:15 PM
Last modification on : Wednesday, February 17, 2021 - 3:05:38 AM
Long-term archiving on: : Sunday, May 16, 2021 - 7:26:11 PM

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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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