12 papers · 1 filter
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…
Finite time blow-up and global solutions for the viscoelastic wave equation with combined power-type nonlinearities
Haiyang Lin, Jinqi Yan, Bo You +1
The main objective of this manuscript is to investigate the global behavior of the solutions to the viscoelastic wave equation with a linear memory term of Boltzmann type, and a no…
Liouville theorems for anisotropic -Laplace equations with a semilinear term
Weizhao Liang, Tian Wu, Jin Yan
In this paper, we investigate Liouville theorems for solutions to the anisotropic -Laplace equation $$-Δ_p^H u=-\operatorname{div}(a(\nabla u))=f(u),\quad\text{in }\mathbb{R}^n,…
Neumann Problems for Elliptic and Parabolic Sum Hessian Equations
Weizhao Liang, Jin Yan, Hua Zhu
This paper studies the Neumann boundary value problem for sum Hessian equations. We first derive a priori estimates for -admissible solutions in almost convex and unif…
The Pogorelov estimates for the sum Hessian equation with rigidity theorem and parabolic versions
Weizhao Liang, Jin Yan, Hua Zhu
In this paper, we primarily study the Pogorelov-type estimates for -convex solutions of the sum Hessian equation under the assumption of semi-convexity, and apply thes…
Classification of positive solutions of critical anisotropic Sobolev equation without the finite volume constraint
Lu Chen, Tian Wu, Jin Yan +1
In this paper, we classify all positive solutions of the critical anisotropic Sobolev equation \begin{equation}\label{0.1} -Δ^{H}_{p}u = u^{p^{*}-1}, \ \ x\in \mathbb{R}^n \end{equ…