Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions (Q1100423)

[For part I, see the authors, ibid. 62, 379-396 (1985; Zbl 0627.49013).] This is the second paper of a series devoted to the study of Hamilton- Jacobi equations in infinite dimensions. Existence results are obtained under much the same assumptions for the corresponding results in finite dimensions. A new convergence theorem concerning the convergence of solutions of the approximate problems is proved and then used to obtain a general existence result. By several reduction processes, the general existence result is reduced to existence for Lipschitz continuous Hamiltonians, which is obtained by the differential game method.