5 papers
Some variational problems for the complex Monge--Amp{è}re operator
Jianchun Chu, Yaxiong Liu, Nicholas McCleerey +1
We consider the Dirichlet problem for the complex Monge--Ampère equation on strongly pseudoconvex Kähler manifolds when the right-hand side is decreasing in the solution. Using flo…
A Decomposition Lemma in Convex Integration via Classical Algebraic Geometry
Zhitong Su, Weijun Zhang
In this paper, we prove a decomposition lemma for symmetric matrix fields on bounded domains: with uniform control on and $a_i…
Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Bounded Domains
Weijun Zhang, Zhitao Zhang
In this paper, we are concerned with the monotonic and symmetric properties of convex solutions to fully nonlinear elliptic systems. We mainly discuss Monge-Ampère type systems for…
Bifurcation on Fully Nonlinear Elliptic Equations and Systems
Jing Gao, Weijun Zhang, Zhitao Zhang
In this paper, we study the following fully nonlinear elliptic equations \begin{equation*} \left\{\begin{array}{rl} \left(S_{k}(D^{2}u)\right)^{\frac1k}=λf(-u) & in\quadΩ\\ u=0 & o…
Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems: Unbounded Domains
Weijun Zhang, Zhitao Zhang
In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Ampère systems for instance, considering \begin{equation*} \det(D^2u^i)=f^i(x,…