The analysis of a function space associated with peridynamics

In this talk I will present recent results on some functional analytic properties of a function space related to a nonlocal model in mechanics. The nonlocal model is made up of a coupled system of integral equations.  The main focus will be the associated energy spaces and their connections with classical function spaces. Conditions that imply compact embedding of these spaces in Lp spaces will be given. Using a fractional Hardy-type inequality, we also establish equivalence of some of these spaces with classical fractional Sobolev spaces. Open problems related to these function spaces and their connection in proving regularity of solutions to systems of integral equations will be discussed.