On L-viscosity solutions of parabolic bilateral obstacle problems with unbounded ingredients

2021 ◽  
Vol 296 ◽  
pp. 724-758
Author(s):  
Shota Tateyama
Keyword(s):  
Viscosity Solutions ◽  
Obstacle Problems

Hölder gradient estimates for fully nonlinear elliptic equations

1988 ◽  
Vol 108 (1-2) ◽  
pp. 57-65 ◽  
Author(s):  
Neil S. Trudinger
Keyword(s):  
Viscosity Solutions ◽  
Elliptic Equations ◽  
Existence Theorems ◽  
Nonlinear Elliptic Equations ◽  
Obstacle Problems ◽  
Gradient Estimates ◽  
Classical Solutions ◽  
Nonlinear Elliptic ◽  
Differential Game Theory ◽  
Special Case

SynopsisIn this paper we prove interior and global Hölder estimates for Lipschitz viscosity solutions of second order, nonlinear, uniformly elliptic equations. The smoothness hypotheses on the operators are more general than previously considered for classical solutions, so that our estimates are also new in this case and readily extend to embrace obstacle problems. In particular Isaac's equations of stochastic differential game theory constitute a special case of our results, and moreover our techniques, in combination with recent existence theorems of Ishii, lead to existence theorems for continuously differentiable viscosity solutions of the uniformly elliptic Isaac's equation.

scholarly journals Root’s barrier, viscosity solutions of obstacle problems and reflected FBSDEs

2015 ◽  
Vol 125 (12) ◽  
pp. 4601-4631 ◽  
Author(s):  
Paul Gassiat ◽  
Harald Oberhauser ◽  
Gonçalo dos Reis
Keyword(s):  
Viscosity Solutions ◽  
Obstacle Problems

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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