Viscosity solutions of eikonal and Lie equations on compact manifolds

1989 ◽  
Vol 7 (2) ◽  
pp. 79-83 ◽  
Author(s):  
Philippe Delano�
Keyword(s):  
Viscosity Solutions ◽  
Compact Manifolds

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.

scholarly journals Hamilton-Jacobi equations in infinite dimensions. II. Existence of viscosity solutions

1986 ◽  
Vol 65 (3) ◽  
pp. 368-405 ◽  
Author(s):  
Michael G Crandall ◽  
Pierre-Louis Lions
Keyword(s):  
Viscosity Solutions ◽  
Infinite Dimensions ◽  
Jacobi Equations
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