5 papers
Regularity for convex viscosity solutions of Equation
Ruosi Chen, Huaiyu Jian, Xushan Tu +1
We prove interior regularity result for convex viscosity solutions of the quadratic Hessian equation , under the assumption that with $\inf…
An Integral Approach to Prescribing Scalar Curvature Equations
Ruosi Chen, Huaiyu Jian, Xingchen Zhou
We develop an integral approach to obtain interior a priori estimates for convex solutions of prescribing scalar curvature equations as well as the Hessia…
Continuity estimates for the gradient of solutions to the Monge-Ampère equation with nature boundary conditions
Huaiyu Jian, Ruixuan Zhu
We study the first derivative estimates for solutions to Monge-Ampère equations in terms of modulus of continuity. As a result, we establish the optimal global log-Lipschitz contin…
Strong maximum principle for generalized solutions to equations of the Monge-Ampère type
Huaiyu Jian, Xushan Tu
In this paper, we investigate the strong maximum principle for generalized solutions of Monge-Ampère type equations. We prove that the strong maximum principle holds at points wher…
The Anisotropic Convexity of Domains and the Boundary Estimate for Two Monge-Ampère Equations
Ruosi Chen, Huaiyu Jian
We study the exact effect of the anisotropic convexity of domains on the boundary estimate for two Monge-Ampère Equations: one is singular which is from the proper affine hypersphe…