PIMS - SFU Computational Mathematics Seminar: James Scott

We consider the Dirichlet problem for a strongly-coupled nonlocal system of equations motivated by peridynamics, a model in continuum mechanics. The strain energy densities involve the magnitude of projected "directional" difference quotients of the displacement. We will describe sufficient conditions on the interaction kernels for the existence and uniqueness of solutions. These conditions extend and generalize previously known sufficient conditions. It turns out that the energy space naturally arising in a certain class of these problems is in fact equivalent to the class of fractional Sobolev spaces. The equivalence can be considered a Korn-type characterization of fractional Sobolev spaces. This equivalence permits us to apply classical Sobolev embeddings in the process of proving that weak solutions to the nonlocal system enjoy both improved differentiability and improved integrability.