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| Boundary Behavior of Large Solutions for Equations of Monge-Amp`ere Type |
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Citation： |
Zhijun ZHANG.Boundary Behavior of Large Solutions for Equations of Monge-Amp`ere Type[J].Chinese Annals of Mathematics B,2026,(2):297~314 |
| Page view： 82
Net amount： 32 |
Authors： |
Zhijun ZHANG; |
Foundation： |
Shandong Provincial Natural Science Foundation (Nos. ZR2021MA007, ZR2022MA020) |
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| Abstract： |
This paper is concerned with the existence and optimal boundary behavior of large solutions to the Monge-Amp`ere type equations det D2u(x)=λun(x)+b(x)g(∣?u(x)∣), x∈Ω, where Ω is a uniformly convex, bounded smooth domain in Rn with n≥2, b∈C∞(Ω) is positive in Ω, g∈C[0,∞)∩C1(0,∞), g(0)=0, g is increasing on [0,∞). The author finds new structure conditions on g which play a crucial role in boundary behavior of such solutions. |
Keywords： |
Monge-Amp`ere type equations A nonlinear gradient term Large convex solutions Boundary behavior |
Classification： |
35J25, 35J92 |
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