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Crandall, Michael G.; Lions, Pierre-Louis

Hamilton-Jacobi equations in infinite dimensions. II: Existence of viscosity solutions. (English) Zbl 0639.49021

J. Funct. Anal. 65, 368-405 (1986).
[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.
Reviewer: S.Lenhart

Cited in 3 Reviews
Cited in 63 Documents

MSC:

49L99 Hamilton-Jacobi theories
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35F30 Boundary value problems for nonlinear first-order PDEs

Keywords:

viscosity solutions; Hamilton-Jacobi equations in infinite dimensions

Citations:

Zbl 0627.49013
PDFBibTeX XMLCite
\textit{M. G. Crandall} and \textit{P.-L. Lions}, J. Funct. Anal. 65, 368--405 (1986; Zbl 0639.49021)
Full Text: DOI

References:

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