Author:
Dai Limei,Cheng Huihui,Li Hongfei
Abstract
AbstractFirst, the symmetry of classical solutions to the Monge–Ampère-type equations is obtained by the moving plane method. Then, the existence and nonexistence of radial solutions in a ball are got from the symmetry results. Finally, the existence and nonexistence of classical solutions to Hessian equations in bounded domains are considered.
Funder
Innovative Research Group Project of the National Natural Science Foundation of China
Natural Science Foundation of Shandong Province
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference40 articles.
1. Guan, P.F., Wang, X.J.: On a Monge–Ampère equation arising in geometric optics. J. Differ. Geom. 48, 205–222 (1998)
2. Graduate Studies in Mathematics;C. Villani,2003
3. Trudinger, N.S.: Recent developments in elliptic partial differential equations of Monge–Ampère type. In: International Congress of Mathematicians, vol.III, pp. 291–301. Eur. Math. Soc., Zürich (2006)
4. Mathematical Surveys and Monographs;Q. Han,2006
5. Gutiérrez, C.E., Huang, Q.B.: The refractor problem in reshaping light beams. Arch. Ration. Mech. Anal. 193, 423–443 (2009)
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