7 papers · 2 filters
Boundary regularity of -Hessian eigenfunctions
Guohuan Qiu, Jin Yan
We prove smoothness up to the boundary for -Hessian eigenfunctions on smooth bounded uniformly convex domains when . This resolves an open problem in the regularity t…
Sharp Hessian integrability for the planar Monge--Ampère equation
XiaoRui Lu, Jin Yan, Bao Yu +1
We determine the optimal local integrability of the Hessian for planar convex Alexandrov solutions satisfying The distributional Hes…
Ground states of a logarithmic Schrödinger equation with a power perturbation in : existence, uniqueness and nondegeneracy
Jinqi Yan, Bo You
The objective of this paper is to study the existence and uniqueness of positive ground state solutions of the following Schrödinger problem \[ -Δu=u\log u^2+μ\abs{u}^{p-1}u\qquad\…
The -Laplace equation with a gradient term II: classification in the second critical case
Tian Wu, Jin Yan, Hua Zhu
Let and . We classify positive, locally bounded weak solutions of \[-Δ_m u=u^p|Du|^q\quad\text{in }\mathbb R^n,\qquad p=\frac{m-q}{n-m}\left(n+\frac{q}{m-1-q}\righ…
Interior estimates for Hessian quotient equations
Guohuan Qiu, Jin Yan
We prove interior Hessian estimates in arbitrary dimensions for admissible solutions of Hessian quotient equations with constant right-hand side, when the numerator and denominator…
Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions
Guohuan Qiu, Jin Yan
We resolve the long-standing problem of establishing interior \(C^2\) estimates for admissible solutions of the graphical scalar curvature equation in every dimension \(n\ge 3\). M…
Interior estimate for semi-convex solutions to a class of Hessian quotient equations in arbitrary dimensions
Xinqun Mei, Jin Yan
In this paper, we study the interior estimates for Hessian quotient equations for , in arbitrary dimensions, under the natur…