Bao, Jiguang; Li, Haigang; Zhang, Lei Global solutions and exterior Dirichlet problem for Monge-Ampère equation in \(\mathbb{R}^2\). (English) Zbl 1374.35188 Differ. Integral Equ. 29, No. 5-6, 563-582 (2016). Summary: Monge-Ampère equation \(\det(D^2u)=f\) in two dimensional spaces is different in nature from their counterparts in higher dimensional spaces. In this article we employ new ideas to establish two main results for the Monge-Ampère equation defined either globally in \(\mathbb{R}^2\) or outside a convex set. First, we prove the existence of a global solution that satisfies a prescribed asymptotic behavior at infinity, if \(f\) is asymptotically close to a positive constant. Then we solve the exterior Dirichlet problem if data are given on the boundary of a convex set and at infinity. Cited in 5 Documents MSC: 35J96 Monge-Ampère equations 35J67 Boundary values of solutions to elliptic equations and elliptic systems Keywords:convex viscosity solution; Perron’s method; radial solution; asymptotic behavior PDFBibTeX XMLCite \textit{J. Bao} et al., Differ. Integral Equ. 29, No. 5--6, 563--582 (2016; Zbl 1374.35188) Full Text: arXiv