Remarks on the existence and uniqueness of unbounded viscosity solutions of Hamilton-Jacobi equations. (English) Zbl 0678.35009

This paper deals with existence and uniqueness questions for unbounded viscosity solutions of general first-order Hamilton-Jacobi equations. The growth condition on the gradient dependence includes power functions. The growth of solutions is limited by exponential functions. Some cases are presented in which non-uniqueness is possible and the existence of minimal solutions is given. The Cauchy problem is treated also, in particular the case without conditions at infinity.
Reviewer: S.Lenhart


35F30 Boundary value problems for nonlinear first-order PDEs
35A05 General existence and uniqueness theorems (PDE) (MSC2000)