A boundary-value problem for Hamilton-Jacobi equations in hilbert spaces

Piermarco Cannarsa, Fausto Gozzi, Halil Mete Soner

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We study a Hamilton-Jacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and state-space constraints. The corresponding boundary conditions for the Hamilton-Jacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finite-dimensional case. We obtain a uniqueness result for viscosity solutions of such a problem and then prove the existence of a solution by showing that the value function is continuous.

Original languageEnglish (US)
Pages (from-to)197-220
Number of pages24
JournalApplied Mathematics & Optimization
Issue number1
StatePublished - Jul 1991
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics


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