Ruosi Chen

activity

20232026

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math.AP2024

New Approach for Interior Regularity of Monge-Ampère Equations

Ruosi Chen, Xingchen Zhou

By developing an integral approach, we present a new method for the interior regularity of strictly convex solution of the Monge-Ampère equation $det D^{2} u = 1$ .

math.AP2024

An Integral Approach to Prescribing Scalar Curvature Equations

Ruosi Chen, Huaiyu Jian, Xingchen Zhou

We develop an integral approach to obtain interior a priori $C^{1, 1}$ estimates for convex solutions of prescribing scalar curvature equations $σ_{2} (κ) = f (x)$ as well as the Hessia…