Huaiyu Jian

Continuity estimates for the Monge-Ampere equation

In this paper, we study the regularity of solutions to the Monge–Ampere equation. We prove the log-Lipschitz continuity for the gradient under certain assumptions. We also give a unified treatment ...

Evolution of Spacelike Hypersurfaces by Mean Curvature Minus External Force Field in Minkowski Space

Abstract We study the evolution of spacelike hypersurface moving by mean curvature minus an external force field in Minkowski space. It is shown that the flow will exist for all time if the initial spacelike surface has two compact spacelike barrier surfaces and the external force field satisfies a weak convexity condition.

Existence of entire solutions to the Monge-Ampère equation

We prove the existence of infinitely many entire convex solutions to the Monge-Amp\`ere equation

Ginzburg-Landau vortices with pinning functions and self-similar solutions in harmonic maps

{\rm det} D^2 u=f

A singular Monge-Ampère equation on unbounded domains

in

The Radial Solutions of Monge-Ampère Equations and the Semi-geostrophic System

{\Bbb R}^n

The Monge–Ampère equation with infinite boundary value

, assuming that the inhomogeneous term

Vortex Dynamics of Ginzburg–Landau Equations in Inhomogeneous Superconductors☆

f\ge 0

Hessian equations with Infinite Dirichlet Boundary Value

and is of polynomial growth at infinity. When

Nonuniqueness of solutions to the Lp-Minkowski problem

f