On uniqueness and existence of viscosity solutions of fully nonlinear second-order elliptic PDE's

Communications on Pure and Applied Mathematics ◽

10.1002/cpa.3160420103 ◽

1989 ◽

Vol 42 (1) ◽

pp. 15-45 ◽

Author(s):

Hitoshi Ishii

Keyword(s):

Viscosity Solutions ◽

Second Order ◽

Fully Nonlinear ◽

Uniqueness And Existence

Download Full-text

Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. III. Uniqueness of viscosity solutions for general second-order equations

Journal of Functional Analysis ◽

10.1016/0022-1236(89)90062-1 ◽

1989 ◽

Vol 86 (1) ◽

pp. 1-18 ◽

Author(s):

P.L Lions

Keyword(s):

Stochastic Control ◽

Viscosity Solutions ◽

Second Order ◽

Optimal Stochastic Control ◽

Infinite Dimensions ◽

Fully Nonlinear ◽

Second Order Equations

Download Full-text

Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2008.21.763 ◽

2008 ◽

Vol 21 (3) ◽

pp. 763-800 ◽

Author(s):

Mariane Bourgoing ◽

Keyword(s):

Boundary Conditions ◽

Viscosity Solutions ◽

Parabolic Equations ◽

Neumann Boundary ◽

Second Order ◽

Neumann Boundary Conditions ◽

Fully Nonlinear

Download Full-text

A uniqueness result for viscosity solutions of second order fully nonlinear partial differential equations

Proceedings of the American Mathematical Society ◽

10.1090/s0002-9939-1988-0934877-2 ◽

1988 ◽

Vol 102 (4) ◽

pp. 975-975 ◽

Author(s):

R. Jensen ◽

P.-L. Lions ◽

P. E. Souganidis

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Viscosity Solutions ◽

Nonlinear Partial Differential Equations ◽

Uniqueness Result ◽

Second Order ◽

Partial Differential ◽

Fully Nonlinear

Download Full-text

On existence and uniqueness of viscosity solutions for second order fully nonlinear PDEs with Caputo time fractional derivatives

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-018-0513-y ◽

2018 ◽

Vol 25 (3) ◽

Author(s):

Tokinaga Namba

Keyword(s):

Viscosity Solutions ◽

Existence And Uniqueness ◽

Fractional Derivatives ◽

Second Order ◽

Nonlinear Pdes ◽

Fully Nonlinear ◽

Fully Nonlinear Pdes

Download Full-text

A representation formula and regularizing properties for viscosity solutions of second-order fully nonlinear degenerate parabolic equations

Nonlinear Analysis ◽

10.1016/0362-546x(94)00170-m ◽

1995 ◽

Vol 24 (2) ◽

pp. 147-158 ◽

Author(s):

Markos A. Katsoulakis

Keyword(s):

Viscosity Solutions ◽

Parabolic Equations ◽

Representation Formula ◽

Second Order ◽

Degenerate Parabolic Equations ◽

Fully Nonlinear ◽

Nonlinear Degenerate Parabolic Equations ◽

Degenerate Parabolic ◽

Nonlinear Degenerate

Download Full-text

Viscosity solutions for fully nonlinear second order equations with applications to stochastic differential games

10.1109/cdc.1986.267218 ◽

1986 ◽

Author(s):

Robert Jensen

Keyword(s):

Differential Games ◽

Viscosity Solutions ◽

Stochastic Differential Games ◽

Second Order ◽

Fully Nonlinear ◽

Second Order Equations

Download Full-text

Viscosity solutions of fully nonlinear second-order elliptic partial differential equations

Journal of Differential Equations ◽

10.1016/0022-0396(90)90068-z ◽

1990 ◽

Vol 83 (1) ◽

pp. 26-78 ◽

Author(s):

H Ishii ◽

P.L Lions

Keyword(s):

Partial Differential Equations ◽

Differential Equations ◽

Viscosity Solutions ◽

Elliptic Partial Differential Equations ◽

Second Order ◽

Partial Differential ◽

Fully Nonlinear

Download Full-text

Viscosity solutions of fully nonlinear second order equations and optimal stochastic control in infinite dimensions. Part II: Optimal control of Zakai's equation

Stochastic Partial Differential Equations and Applications II - Lecture Notes in Mathematics ◽

10.1007/bfb0083943 ◽

1989 ◽

pp. 147-170 ◽

Author(s):

P. L. Lions

Keyword(s):

Optimal Control ◽

Stochastic Control ◽

Viscosity Solutions ◽

Second Order ◽

Optimal Stochastic Control ◽

Infinite Dimensions ◽

Fully Nonlinear ◽

Second Order Equations

Download Full-text

Viscosity solutions of fully nonlinear second order parabolic equations with $L^1$ dependence in time and Neumann boundary conditions. Existence and applications to the level-set approach

Discrete and Continuous Dynamical Systems ◽

10.3934/dcds.2008.21.1047 ◽

2008 ◽

Vol 21 (4) ◽

pp. 1047-1069 ◽

Author(s):

Mariane Bourgoing ◽

Keyword(s):

Boundary Conditions ◽

Level Set ◽

Viscosity Solutions ◽

Parabolic Equations ◽

Neumann Boundary ◽

Second Order ◽

Neumann Boundary Conditions ◽

Fully Nonlinear ◽

Level Set Approach

Download Full-text

Viscosity solutions of fully nonlinear second-order equations and optimal stochastic control in infinite dimensions. Part I: the case of bounded stochastic evolutions

Acta Mathematica ◽

10.1007/bf02392299 ◽

1988 ◽

Vol 161 (0) ◽

pp. 243-278 ◽

Author(s):

P. L. Lions

Keyword(s):

Stochastic Control ◽

Viscosity Solutions ◽

Second Order ◽

Optimal Stochastic Control ◽

Infinite Dimensions ◽

Fully Nonlinear ◽

Second Order Equations

Download Full-text