Applied Mathematics and Optimization

, Volume 24, Issue 1, pp 197–220

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


  • Piermarco Cannarsa
    • Dipartimento di Matematica
  • Fausto Gozzi
    • Scuola Normale Superiore
  • Halil Mete Soner
    • Department of MathematicsCarnegie-Mellon University

DOI: 10.1007/BF01447742

Cite this article as:
Cannarsa, P., Gozzi, F. & Soner, H.M. Appl Math Optim (1991) 24: 197. doi:10.1007/BF01447742


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.

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© Springer-Verlag New York Inc. 1991