Exterior nonlocal variational inequalities associated with the fractional laplace operator

This paper introduces a new class of variational inequalities where the obstacle is placed in the exterior domain that is disjoint from the observation domain. This is carried out with the help of nonlocal fractional operators. The need for such novel variational inequalities stems from the fact that the classical approach only allows placing the obstacle either inside the observation domain or on the boundary. An analysis of the continuous problem is provided. Additionally, penalization arguments to approximate the problem are discussed.