On asymptotic exit-time control problems lacking coercivity
ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 957-982.

The research on a class of asymptotic exit-time problems with a vanishing Lagrangian, begun in [M. Motta and C. Sartori, Nonlinear Differ. Equ. Appl. Springer (2014).] for the compact control case, is extended here to the case of unbounded controls and data, including both coercive and non-coercive problems. We give sufficient conditions to have a well-posed notion of generalized control problem and obtain regularity, characterization and approximation results for the value function of the problem.

DOI : 10.1051/cocv/2014003
Classification : 49J15, 49N25, 93C10, 49L20, 49L25, 93D20
Mots-clés : exit-time problems, impulsive optimal control problems, viscosity solutions, asymptotic controllability 
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     title = {On asymptotic exit-time control problems lacking coercivity},
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     pages = {957--982},
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Motta, M.; Sartori, C. On asymptotic exit-time control problems lacking coercivity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 20 (2014) no. 4, pp. 957-982. doi : 10.1051/cocv/2014003. http://www.numdam.org/articles/10.1051/cocv/2014003/

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