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A boundaryvalue problem for HamiltonJacobi equations in hilbert spaces
 Piermarco Cannarsa,
 Fausto Gozzi,
 Halil Mete Soner
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Abstract
We study a HamiltonJacobi equation in infinite dimensions arising in optimal control theory for problems involving both exit times and statespace constraints. The corresponding boundary conditions for the HamiltonJacobi equation, of mixed nature, have been derived and investigated in [19], [2], [5], and [15] in the finitedimensional 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.
The work of P. Cannarsa was partially supported by the Italian National Project “Equazioni Differenziali e Calcolo delle Variazioni”. H. M. Soner's work was supported by National Science Foundation Grant DMS9002249.
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 Title
 A boundaryvalue problem for HamiltonJacobi equations in hilbert spaces
 Journal

Applied Mathematics and Optimization
Volume 24, Issue 1 , pp 197220
 Cover Date
 19910701
 DOI
 10.1007/BF01447742
 Print ISSN
 00954616
 Online ISSN
 14320606
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Authors

 Piermarco Cannarsa ^{(1)}
 Fausto Gozzi ^{(2)}
 Halil Mete Soner ^{(3)}
 Author Affiliations

 1. Dipartimento di Matematica, Via F. Buonarroti 2, 57127, Pisa, Italy
 2. Scuola Normale Superiore, 56126, Pisa, Italy
 3. Department of Mathematics, CarnegieMellon University, 15213, Pittsburgh, PA, USA