The value function of an optimal stopping problem for jump diffusions is
known to be a generalized solution of a variational inequality. Assuming that
the diffusion component of the process is nondegenerate and a mild assumption
on the singularity of the L\'{e}vy measure, this paper shows that the value
function of this optimal stopping problem on an unbounded domain with
finite/infinite variation jumps is in Wp,loc2,1​ with p∈(1,∞). As a consequence, the smooth-fit property holds.Comment: To Appear in the SIAM Journal on Control and Optimizatio