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# Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation

Abstract : We prove sharp uniform estimates for strong supersolutions of a large class of fully nonlinear degenerate elliptic complex equations. Our findings rely on ideas of Kuo and Trudinger who dealt with degenerate linear equations in the real setting. We also exploit the pluripotential theory for the complex Monge-Ampère operator as well as suitably tailored theory of $L^p$-viscosity subsolutions.
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Cited literature [36 references]

https://hal.archives-ouvertes.fr/hal-02973743
Contributor : Guillaume Olive Connect in order to contact the contributor
Submitted on : Wednesday, November 4, 2020 - 7:25:11 AM
Last modification on : Tuesday, December 7, 2021 - 3:33:15 PM

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maximum_principle.pdf
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• HAL Id : hal-02973743, version 2

### Citation

Soufian Abja, Sławomir Dinew, Guillaume Olive. Uniform estimates for concave homogeneous complex degenerate elliptic equations comparable to the Monge-Ampère equation. 2020. ⟨hal-02973743v2⟩

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