Existence results for first order Hamilton Jacobi equations
Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 5, p. 325-340 
@article{AIHPC_1984__1_5_325_0,
     author = {Barles, Guy},
     title = {Existence results for first order Hamilton Jacobi equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {1},
     number = {5},
     year = {1984},
     pages = {325-340},
     zbl = {0574.70019},
     mrnumber = {779871},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1984__1_5_325_0}
}

Barles, G. Existence results for first order Hamilton Jacobi equations. Annales de l'I.H.P. Analyse non linéaire, Volume 1 (1984) no. 5, pp. 325-340. http://www.numdam.org/item/AIHPC_1984__1_5_325_0/

[1] S.H. Benton, The Hamilton Jacobi Equation. A global Approach, Academic Press, New York, 1977. | MR 442431 | Zbl 0418.49001

[2] E.D. Conway and E. Hopf, Hamilton's theory and generalized solutions of Hamilton Jacobi equations. J. Math. Mech., t. 12, 1964, p. 939-986. | MR 182761 | Zbl 0178.11002

[3] M.G. Crandall, L.C. Evans, P.L. Lions, Some properties of viscosity solutions of Hamilton Jacobi equations. To appear in Trans. Amer. Math. Soc., 1983. | MR 732102 | Zbl 0543.35011

[4] M.G. Crandall and P.L. Lions, Viscosity solutions of Hamilton Jacobi equations. To appear in Trans. Amer. Math. Soc., 1983. | MR 690039 | Zbl 0599.35024

[5] A. Douglis, The continuous dependance of generalized solutions of non linear partial differential equations upon initial data. Comm. Pure Applied Math., t. 14, 1961, p. 267-284. | MR 139848 | Zbl 0117.31102

[6] W.H. Fleming, The Cauchy problem for a non linear partial differential. J. Diff. equations, t. 5, 1969, p. 515-530. | MR 235269 | Zbl 0172.13901

[7] W.H. Fleming, Nonlinear partial differential equations-probabilistie and game theoretic method. In Problems in Nonlinear Analysis, CIME Ed. Cremonese, Roma, 1971. | MR 282048 | Zbl 0225.35020

[8] W.H. Fleming, The Cauchy problem for degenerate parabolic equations. J. Math. Mech., t. 13, 1964, p. 987-1008. | MR 179473 | Zbl 0192.19602

[9] A. Friedman, The Cauchy problem for first order partial differential equations. Indiana Univ. Mat. J., t. 23, 1973, p. 27-40. | MR 326136 | Zbl 0243.35014

[10] S.N. Kruzkov, Generalized solutions of Hamilton Jacobi equations of Eikonal type. I. USSR Sbornik, t. 27, 1975, p. 406-446. | Zbl 0369.35012

[11] S.N. Kruzkov, Generalized solutions of nonlinear first order equations and certain quasilinear parabolic equations Vestnik Moscow unio Ser. I. Math. Mech., t. 6, 1964, p. 67-74 (In Russian).

[12] S.N. Kruskov, Generalized solutions of first order nonlinear equations in several independant variables. I. Mat. Sb., t. 70, 112, 1966, p. 394-415, II. Mat. Sb. (N. S.), t. 72, 114, 1967, p. 93-116 (in Russian). | Zbl 0164.40802

[13] P.L. Lions, Generalized solutions of Hamilton Jacobi equations. Pitman London, 1982, | MR 667669 | Zbl 0497.35001

[14] P.L. Lions, Existence results for first order Hamilton Jacobi equations. To appear in Ric. Mat. | MR 740198 | Zbl 0552.70012

[15] P.E. Souganidis, Existence of viscosity solutions of Hamilton Jacobi equations. | Zbl 0506.35020