A priori estimates for the complex Monge-Amp\`ere equation after Krylov
S{\l}awomir Dinew, Marcin Sroka
TL;DR
This paper provides analytic proofs for Krylov's $C^{1,1}$ estimates and Bedford-Taylor interior estimates for solutions to the degenerate complex Monge-Ampère equation, advancing understanding of regularity in complex analysis.
Contribution
It offers new analytic proofs for key regularity estimates in the degenerate complex Monge-Ampère equation, previously established through different methods.
Findings
Proof of Krylov $C^{1,1}$ estimates for degenerate complex Monge-Ampère solutions
Analytic proof of Bedford-Taylor interior $C^{1,1}$ estimate
Enhanced understanding of regularity properties in complex Monge-Ampère equations
Abstract
We establish an analytic proof for the Krylov estimates for solutions of degenerate complex Monge-Amp\`ere equation. We also provide an analytic proof of the Bedford-Taylor interior estimate.
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