Local H\"older continuity of solutions of the complex Monge-Amp\`ere equation
Nguyen Xuan Hong, Pham Thi Lieu
TL;DR
This paper investigates the conditions under which solutions to the complex Monge-Ampère equation are locally Hölder continuous, focusing on the Dirichlet problem and establishing necessary and sufficient criteria.
Contribution
It provides a complete characterization of when the Dirichlet problem for the complex Monge-Ampère operator admits Hölder continuous solutions.
Findings
Established necessary and sufficient conditions for Hölder continuity
Characterized the regularity of solutions to the complex Monge-Ampère equation
Enhanced understanding of boundary regularity in complex analysis
Abstract
In this paper, we are interested in studying the Dirichlet problem for the complex Monge-Amp\`ere operator. We provide necessary and sufficient conditions for the problem to have H\"older continuous solutions.
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