Remarks on existence of viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0546.35042

Ishii, Hitoshi

Bull. Fac. Sci. Eng., Chuo Univ., Ser. I 26, 5-24 (1983).

The author considers the classical first-order Hamilton-Jacobi equations and proves existence theorems for stationary and Cauchy problems. All the results and methods are based upon the notion of viscosity solutions introduced by M. G. Crandall and the reviewer. They extend (to the UC case) the existence results first obtained by the reviewer and by G. Bailes. One may also quote the independent works of M. G. Grandall and the reviewer where similar results are proved.

Reviewer: P.L.Lions

MSC:

35L60	First-order nonlinear hyperbolic equations
35A05	General existence and uniqueness theorems (PDE) (MSC2000)
70H20	Hamilton-Jacobi equations in mechanics

Keywords:

modulus of continuity; Hamilton-Jacobi equations; existence; Cauchy problems; viscosity solutions