Radial solutions of a Neumann problem coming from a burglary model

2015 ◽  
pp. 257-268
Author(s):  
M. Garcia-Huidobro ◽  
R. Manásevich ◽  
J. Mawhin
Keyword(s):  
Neumann Problem ◽  
Radial Solutions

scholarly journals Multi-layer radial solutions for a supercritical Neumann problem

2016 ◽  
Vol 261 (1) ◽  
pp. 455-504 ◽  
Author(s):  
Denis Bonheure ◽  
Massimo Grossi ◽  
Benedetta Noris ◽  
Susanna Terracini
Keyword(s):  
Neumann Problem ◽  
Radial Solutions

scholarly journals The exterior Dirichlet problems of Monge–Ampère equations in dimension two

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Limei Dai
Keyword(s):  
Asymptotic Behavior ◽  
Unit Ball ◽  
Bounded Domain ◽  
Viscosity Solutions ◽  
Sufficient Conditions ◽  
Radial Solutions ◽  
Dirichlet Problems ◽  
Necessary And Sufficient ◽  
Monge Ampere ◽  
Prescribed Asymptotic Behavior

AbstractIn this paper, we study the Monge–Ampère equations $\det D^{2}u=f$ det D 2 u = f in dimension two with f being a perturbation of $f_{0}$ f 0 at infinity. First, we obtain the necessary and sufficient conditions for the existence of radial solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a unit ball. Then, using the Perron method, we get the existence of viscosity solutions with prescribed asymptotic behavior at infinity to Monge–Ampère equations outside a bounded domain.

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