Calculus of Variations and Geometric Measure Theory
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K. Craig - I. Topaloglu

Convergence of regularized nonlocal interaction energies

created by topaloglu1 on 03 Aug 2019

[BibTeX]

preprint

Inserted: 3 aug 2019

Year: 2015

ArXiv: 1503.04826 PDF

Abstract:

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

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