In:
Bulletin of the Australian Mathematical Society, Cambridge University Press (CUP)
Abstract:
We consider the growth of the convex viscosity solution of the Monge–Ampère equation $\det D^2u=1$ outside a bounded domain of the upper half space. We show that if u is a convex quadratic polynomial on the boundary $\{x_n=0\}$ and there exists some $\varepsilon〉0$ such that $u=O(|x|^{3-\varepsilon })$ at infinity, then $u=O(|x|^2)$ at infinity. As an application, we improve the asymptotic result at infinity for viscosity solutions of Monge–Ampère equations in half spaces of Jia, Li and Li [‘Asymptotic behavior at infinity of solutions of Monge–Ampère equations in half spaces’, J. Differential Equations 269 (1) (2020), 326–348].
Type of Medium:
Online Resource
ISSN:
0004-9727
,
1755-1633
DOI:
10.1017/S000497272300028X
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
2023
detail.hit.zdb_id:
2268688-5
SSG:
17,1
