Qiang Du
Columbia University
Title
Integral equations with nonlocal operators: applications and recent development
Abstract
Recent applications and theoretical developments of integral models using nonlocal operators have shown promise as effective alternatives to local models, especially in dealing with singularities and anomalies. These models also serve as continuum limits for large-scale discrete models used in learning data and network analysis. For models defined on bounded domains, a key challenge lies in the proper mathematical formulation near or at the domain boundaries. We explore various options for imposing appropriate local or nonlocal boundary conditions that complement the nonlocal interactions within the domain's interior. Additionally, we discuss recent advances in the mathematical and numerical analysis of these problems and their applications.
