7 papers
Sharp Boundary Recession Criteria for the Special Lagrangian Curvature Potential Equation
Rongli Huang, Qinfeng Jiang
We establish boundary second derivative estimates for convex graphical solutions of the special Lagrangian curvature potential equation. Since the curvature matrix depends on both…
Existence of non-radial entire solutions for the Hénon equation beyond even exponents
Qinfeng Jiang, Jingang Xiong
This paper is concerned with the existence of non-radial positive classical solutions for the critical Hénon equation \[ -Îu=|x|^αu^{\frac{N+2+2α}{N-2}} \qquad \text{in }\mathb…
Existence and Nonexistence for Hessian Exterior Dirichlet Problems with \(k\)-Admissible Asymptotic Matrices
Jiguang Bao, Qinfeng Jiang
We study exterior Dirichlet problems for \(k\)-Hessian equations with prescribed quadratic asymptotics, allowing the asymptotic matrix to be merely \(k\)-admissible and not necessa…
Optimal Asymptotic Behavior at Infinity for Solutions of the Supercritical Lagrangian Mean Curvature Equation in Exterior Domains
Jiguang Bao, Qinfeng Jiang
We study the asymptotic behavior at infinity of solutions to the supercritical Lagrangian mean curvature equation \[ \sum_{i=1}^n \arctan λ_i(D^2u)=θ+f(x) \] on exterior domains…
The mean curvature type hypersurfaces with prescribed gradient image
Jiguang Bao, Rongli Huang, Qinfeng Jiang
In this paper, we consider the existence of mean curvature type hypersurfaces with prescribed gradient image. Let and be uniformly convex bounded domains in $\mathb…
On the second boundary value problem for Lagrangian mean curvature type equation
Jiguang Bao, Qinfeng Jiang
This article is concerned with the second boundary value problem of the Lagrangian mean curvature type equation arising from special Lagrangian geometry. By the parabolic method, w…