Entropy penalization methods for Hamilton–Jacobi equations

Anantharaman, 2004, On the zero-temperature or vanishing viscosity limit for certain Markov processes arising from Lagrangian dynamics, J. Eur. Math. Soc. (JEMS), 6, 207, 10.4171/JEMS/9 Barles, 1991, Convergence of approximation schemes for fully nonlinear second order equations, Asymptot. Anal., 4, 271, 10.3233/ASY-1991-4305 Camilli Cannarsa, 2004, Semiconcave Functions, Hamilton–Jacobi Equations, and Optimal Control, vol. 58 Capuzzo Dolcetta, 2002, The Hopf solution of Hamilton–Jacobi equations, 343 Capuzzo Dolcetta, 2003, Representations of solutions of Hamilton–Jacobi equations, vol. 54, 79 Crandall, 1992, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27, 1, 10.1090/S0273-0979-1992-00266-5 Dragoni, 2007, Metric Hopf–Lax formula with semicontinuous data, Discrete Contin. Dyn. Syst., 17, 713, 10.3934/dcds.2007.17.713 Dunford, 1958, Linear Operators. I. General Theory, vol. 7 Evans, 1992, Measure Theory and Fine Properties of Functions Evans, 1998, Partial Differential Equations, vol. 19 Evans, 2004, A survey of entropy methods for partial differential equations, Bull. Amer. Math. Soc. (N.S.), 41, 409, 10.1090/S0273-0979-04-01032-8 Fleming, 1986, A PDE approach to some large deviations problems, vol. 23, 441 Gomes, 2005, Viscosity solution methods and the discrete Aubry–Mather problem, Discrete Contin. Dyn. Syst., 13, 103, 10.3934/dcds.2005.13.103 Jordan, 1998, The variational formulation of the Fokker–Planck equation, SIAM J. Math. Anal., 29, 1, 10.1137/S0036141096303359 Mather, 1991, Action minimizing invariant measures for positive definite Lagrangian systems, Math. Z., 207, 169, 10.1007/BF02571383 Mather, 1994, Action minimizing orbits in Hamiltonian systems, vol. 1589, 92 Souganidis, 1985, Approximation schemes for viscosity solutions of Hamilton–Jacobi equations, J. Differential Equations, 59, 1, 10.1016/0022-0396(85)90136-6 Taylor, 1958 Villani, 2003, Topics in Optimal Transportation, vol. 58