Bridging local and nonlocal models: Convergence and regularity

Abstract

As nonlocal models become more widespread in applications, we focus on their connections with their classical counterparts and also on some theoretical aspects which impact their implementation. In this context we survey recent developments by the authors and prove some new results on regularity of solutions to nonlinear systems in the nonlocal framework. In particular, we focus on semilinear problems and also on higher-order problems with applications in the theory of plate deformations.