Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type

Authors
Albano, P Cannarsa, P Sinestrari, C
Citation
P. Albano et al., Regularity results for the minimum time function of a class of semilinear evolution equations of parabolic type, SIAM J CON, 38(3), 2000, pp. 916-946
Citations number
28
Categorie Soggetti
Mathematics,"Engineering Mathematics
Journal title
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
ISSN journal
03630129 → ACNP
Volume
38
Issue
3
Year of publication
2000
Pages
916 - 946
Database
ISI
SICI code
0363-0129(20000316)38:3<916:RRFTMT>2.0.ZU;2-8
Abstract
Under suitable controllability and smoothness assumptions, the minimum time function T(x) of a semilinear control system is proved to be locally Lipsc hitz continuous and semiconcave on the controllable set. These properties a re then applied to derive optimality conditions relating optimal trajectori es to the superdifferential of T.