Discontinuous viscosity solutions of deterministic optimal control problems
Guy Barles, Benoı̂t Perthame · 1986
We study optimal stopping time problems with a discontinuous stopping cost Y. When Y is upper semicontinuous, we show that the lower semi-continuous envelope of the value function is the unique l.s.c. viscosity solution of the associated variational inequality. Using this result we may treat some particular exit time problems.