An application of approximation to comparison principles for viscosity solutions of curvature equations

2006 ◽  
Vol 64 (6) ◽  
pp. 1236-1254 ◽  
Author(s):  
Y. Luo ◽  
A. Eberhard
Keyword(s):  
Viscosity Solutions ◽  
Comparison Principles

scholarly journals Coupling Lévy measures and comparison principles for viscosity solutions

2019 ◽  
Vol 372 (10) ◽  
pp. 7327-7370
Author(s):  
Nestor Guillen ◽  
Chenchen Mou ◽  
Andrzej Świȩch
Keyword(s):  
Viscosity Solutions ◽  
Comparison Principles ◽  
Lévy Measures

scholarly journals Viscosity solutions for a polymer crystal growth model

2011 ◽  
Vol 60 (3) ◽  
pp. 895-936
Author(s):  
Pierre Cardaliaguet ◽  
Olivier Ley ◽  
Aurelien Monteillet
Keyword(s):  
Crystal Growth ◽  
Growth Model ◽  
Viscosity Solutions ◽  
Polymer Crystal

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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