Convergence of Regularized Nonlocal Interaction Energies

Inspired by numerical studies of the aggregation equation, we study the effect of regularization on nonlocal interaction energies. We consider energies defined via a repulsiveattractive interaction kernel, regularized by convolution with a mollifier. We prove that, with respect to the 2-Wasserstein metric, the regularized energies Γ-converge to the unregularized energy and minimizers converge to minimizers. We then apply our results to prove Γ-convergence of the gradient flows, when restricted to the space of measures with bounded density.

• Type: Journal
• Year: 2016
• Where: SIAMMA
• Authors: Katy Craig, Ihsan Topaloglu
• Keywords: Computer Graphics, SIAMMA 2016