The nonlocal inverse problem of Donsker and Varadhan

Abstract

In this paper we prove a version of the celebrated Inverse Problem of Donsker and Varadhan [13] in the setting of nonlocal elliptic operators of the formLu=LKu+BK(h,u), where LK is a uniformly elliptic nonlocal operator with smooth coefficients, and, for h:RN→R smooth and bounded, BK(h,u) is the associated bilinear form, which can be regarded as a nonlocal transport term.