Solvability of Dirichlet problem with Integro-differential Operator

Abstract

This paper studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the continuity set of the exit time operators under Skorohod topology.

24 pages, 3 figures, To appear in SIAM Journal on Control and Optimization