Boundary behavior of solutions of Monge–Ampère equations with singular righthand sides☆
作者： Dongsheng Li , Shanshan Ma
DOI: 10.1016/J.JMAA.2017.04.074
关键词: Boundary (topology) 、 Mathematical analysis 、 Mathematics 、 Ampere 、 Regular polygon 、 Variation theory
摘要: Abstract In this paper, by Karamata regular variation theory and constructing super subsolutions, we obtain the asymptotic boundary behavior of convex solutions Monge–Ampere equations with singular righthand sides.
sci-hub.se 参考文章(22)
Vojislav Marić, Regular Variation and Differential Equations ,(2000)
CHARLES LOEWNER, LOUIS NIRENBERG, Partial Differential Equations Invariant under Conformal or Projective Transformations Contributions to Analysis#R##N#A Collection of Papers Dedicated to Lipman Bers. pp. 245- 272 ,(1974) , 10.1016/B978-0-12-044850-0.50027-7
Neil S Trudinger, David G Gilbarg, Elliptic Partial Differential Equations of Second Order ,(2018)
Zhijun Zhang, Boundary behavior of large solutions to the Monge-Ampère equations with weights Journal of Differential Equations. ,vol. 259, pp. 2080- 2100 ,(2015) , 10.1016/J.JDE.2015.03.040
A.C. Lazer, P.J. McKenna, On Singular Boundary Value Problems for the Monge–Ampére Operator Journal of Mathematical Analysis and Applications. ,vol. 197, pp. 341- 362 ,(1996) , 10.1006/JMAA.1996.0024
Sidney I. Resnick, Extreme Values, Regular Variation, and Point Processes ,(1987)
Zhijun Zhang, The asymptotic behaviour of the unique solution for the singular Lane–Emden–Fowler equation Journal of Mathematical Analysis and Applications. ,vol. 312, pp. 33- 43 ,(2005) , 10.1016/J.JMAA.2005.03.023
Shiu-Yuen Cheng, Shing-Tung Yau, On the regularity of the monge-ampère equation det (∂2 u/∂xi ∂xj) = f(x, u) Communications on Pure and Applied Mathematics. ,vol. 30, pp. 41- 68 ,(1977) , 10.1002/CPA.3160300104
A. C. Lazer, P. J. McKenna, On a singular nonlinear elliptic boundary-value problem Proceedings of the American Mathematical Society. ,vol. 111, pp. 721- 730 ,(1991) , 10.1090/S0002-9939-1991-1037213-9
Florica-Corina Cı̂rstea, Vicenţiu Rădulescu, Uniqueness of the blow-up boundary solution of logistic equations with absorbtion Comptes Rendus Mathematique. ,vol. 335, pp. 447- 452 ,(2002) , 10.1016/S1631-073X(02)02503-7