Non-linear Partial Differential Equations, Viscosity Solution Method in

[1]  H. Ishii.  Perron’s method for Hamilton-Jacobi equations , 1987 .

[2]  Serge Vlăduţ,et al.  Singular viscosity solutions to fully nonlinear elliptic equations , 2008 .

[3]  Antonino Maugeri,et al.  Elliptic and Parabolic Equations with Discontinuous Coefficients , 2000 .

[4]  L. Caffarelli,et al.  Fully Nonlinear Elliptic Equations , 1995 .

[5]  A. Swiech,et al.  Maximum principle for fully nonlinear equations via the iterated comparison function method , 2007 .

[6]  On the state constraint problem for differential games , 1995 .

[7]  W. Fleming,et al.  Deterministic and Stochastic Optimal Control , 1975 .

[8]  D. Gilbarg,et al.  Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[9]  Serge Vlăduţ,et al.  Nonclassical Solutions of Fully Nonlinear Elliptic Equations , 2007, 0912.3119.

[10]  Régis Monneau,et al.  Dislocation Dynamics: Short-time Existence and Uniqueness of the Solution , 2006 .

[11]  W. Fleming,et al.  Controlled Markov processes and viscosity solutions , 1992 .

[12]  M. Bardi,et al.  On the Dirichlet problem for non-totally degenerate fully nonlinear elliptic equations , 2006 .

[13]  P. Souganidis,et al.  Blow-Up of solutions of hamilton-jacobi equations , 1986 .

[14]  P. Lions,et al.  Some Properties of Viscosity Solutions of Hamilton-Jacobi Equations. , 1984 .

[15]  L. Evans,et al.  C1,α regularity for infinity harmonic functions in two dimensions , 2008 .

[16]  Panagiotis E. Souganidis,et al.  Uniqueness of weak solutions of fully nonlinear stochastic partial differential equations , 2000 .

[17]  Luis A. Caffarelli,et al.  On viscosity solutions of fully nonlinear equations with measurable ingredients , 1996 .

[18]  Panagiotis E. Souganidis,et al.  Correctors for the homogenization of Hamilton‐Jacobi equations in the stationary ergodic setting , 2003 .

[19]  P. Lions.  Generalized Solutions of Hamilton-Jacobi Equations , 1982 .

[20]  G. Barles.  Discontinuous viscosity solutions of first-order Hamilton-Jacobi equations: a guided visit , 1993 .

[21]  G. Barles,et al.  Discontinuous solutions of deterministic optimal stopping time problems , 1987 .

[22]  R. Bellman.  Dynamic programming. , 1957, Science.

[23]  Juan J. Manfredi,et al.  A VERSION OF THE HOPF-LAX FORMULA IN THE HEISENBERG GROUP , 2002 .

[24]  P. Lions.  Bifurcation and optimal stochastic control , 1983 .

[25]  P. Souganidis,et al.  Fully nonlinear stochastic partial differential equations , 1998 .

[26]  M. Bardi,et al.  Optimal Control and Viscosity Solutions of Hamilton-Jacobi-Bellman Equations , 1997 .

[27]  M. Crandall,et al.  A TOUR OF THE THEORY OF ABSOLUTELY MINIMIZING FUNCTIONS , 2004 .

[28]  R. Jensen.  The maximum principle for viscosity solutions of fully nonlinear second order partial differential equations , 1988 .

[29]  Xavier Cabré,et al.  Interior C2,α regularity theory for a class of nonconvex fully nonlinear elliptic equations , 2003 .

[30]  L. Evans.  Periodic homogenisation of certain fully nonlinear partial differential equations , 1992, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[31]  R. Jensen.  Uniqueness of Lipschitz extensions: Minimizing the sup norm of the gradient , 1993 .

[32]  L. Caffarelli.  Interior a priori estimates for solutions of fully non-linear equations , 1989 .

[33]  G. Barles.  Solutions de viscosité des équations de Hamilton-Jacobi , 1994 .

[34]  Y. Giga.  Viscosity solutions with shocks , 2001 .

[35]  Cristian E. Gutiérrez,et al.  The Monge―Ampère Equation , 2001 .

[36]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

[37]  Panagiotis E. Souganidis,et al.  Homogenization of fully nonlinear, uniformly elliptic and parabolic partial differential equations in stationary ergodic media , 2005 .

[38]  H. Soner.  Optimal control with state-space constraint I , 1986 .

[39]  S. Shreve,et al.  Methods of Mathematical Finance , 2010 .

[40]  S. Sritharan,et al.  Bellman equations associated to the optimal feedback control of stochastic Navier‐Stokes equations , 2005 .

[41]  G. Barles,et al.  A New Approach to Front Propagation Problems: Theory and Applications , 1998 .