8 papers · 1 filter
A Local Lewy Theorem for -Harmonic Function with Non-zero Gradient in
Jiahuan Li, Yilu Liu, Xi-Nan Ma
We establish a local Lewy-type theorem for \(p\)-harmonic function with non-zero gradient in dimension three space . Let \(1<p<\infty\), and let \(u\in W^{1,p}_{\mathrm{loc}}(…
Nonconvex Sublevel Sets For The Planar Translating Mean Curvature Equation
Jiahuan Li, Yilu Liu, Xi-Nan Ma +1
Translating solitons arise as models for type~II singularities of mean-convex mean curvature flow. We construct a smooth bounded uniformly convex domain \(\Om\Subset\R^2\) such tha…
Brunn--Minkowski Inequality for the First Complex -Hessian Eigenvalue
Chuanqiang Chen, Jiahuan Li, Xi-Nan Ma
There are relatively few results on the convexity of solutions to complex equations. In this paper, We prove a strict real log-concavity theorem for the first eigenfunction of the…
A Brunn--Minkowski inequality for the Hessian eigenvalue in convex domain
Jiahuan Li, Xi-Nan Ma, Paolo Salani
We use the deformation methods to obtain the strictly log concavity of solution of a class Hessian equation in bounded convex domain in , as an application we get t…
The exterior Dirichlet problem for the homogeneous -Hessian equation
Xi-Nan Ma, Dekai Zhang
We study the exterior Dirichlet problem for the homogeneous -Hessian equation. The prescribed asymptotic behavior at infinity of the solution is zero if , it is $…
The Neumann Problem for Hessian Equations
Xi-Nan Ma, Guohuan Qiu
In this paper, we prove the existence of a classical solution to a Neumann boundary problem for Hessian equations in uniformly convex domain. The methods depend upon the establishe…