Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899123 | Journal of Differential Equations | 2018 | 34 Pages |
Abstract
In this paper, we obtain conditions about the existence and boundary behavior of (strictly) convex solutions to the Monge-Ampère equations with boundary blow-updetâ¡D2u(x)=b(x)f(u(x))±|âu|q,xâΩ,u|âΩ=+â, anddetâ¡D2u(x)=b(x)f(u(x))(1+|âu|q),xâΩ,u|âΩ=+â, where Ω is a strictly convex, bounded smooth domain in RN with Nâ¥2, qâ[0,N] (or qâ[0,N)), bâCâ(Ω) which is positive in Ω, but may vanish or blow up on the boundary, fâC[0,â), f(0)=0, and f is strictly increasing on [0,â) (or fâC(R), f(s)>0,âsâR, and f is strictly increasing on R).
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Zhijun Zhang,