On asymptotic exit-time control problems lacking coercivity∗
Received: 2 July 2013
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.
Mathematics Subject Classification: 49J15 / 49N25 / 93C10 / 49L20 / 49L25 / 93D20
Key words: Exit-time problems / impulsive optimal control problems / viscosity solutions / asymptotic controllability
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