Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems:
Unbounded Domains
Symmetry of Convex Solutions to Fully Nonlinear Elliptic Systems:
Unbounded Domains
In this paper, we are concerned with the monotonic and symmetric properties of convex solutions Monge-Amp\`ere systems for instance, considering \begin{equation*} \det(D^2u^i)=f^i(x,{\bf u},\nabla u^i), \ 1\leq i\leq m, \end{equation*} over unbounded domains of various cases, including the whole spaces $\mathbb{R}^n$, the half spaces $\mathbb{R}^n_+$ and the unbounded tube shape domains …