Acta Mathematica Sinica, English Series

, Volume 35, Issue 7, pp 1190–1204 | Cite as

Boundary Behavior of Large Solutions to the Monge-Ampère Equation in a Borderline Case

  • Zhi Jun ZhangEmail author


This paper is concerned with the boundary behavior of strictly convex large solutions to the Monge-Ampère equation detD2u(x) = b(x)f (u(x)), u > 0, x ∈ Ω, where Ω is a strictly convex and bounded smooth domain in ℝN with N ≥ 2, f is normalized regularly varying at infinity with the critical index N and has a lower term, and bC (Ω) is positive in Ω, but may be appropriate singular on the boundary.


The Monge-Ampère equations strictly convex large solutions a borderline case boundary behavior 

MR(2010) Subject Classification

35J60 35B40 35J67 35B65 


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© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.School of Mathematics and Information ScienceYantai UniversityYantaiP. R. China

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