A comparison between the nonlocal and the classical worlds: minimal surfaces, phase transitions, and geometric flows

2020/03/30 by Dipierro, Serena
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2003.13234

Abstract

The nonlocal world presents an abundance of surprises and wonders to discover. These special properties of the nonlocal world are usually the consequence of long-range interactions, which, especially in presence of geometric structures and nonlinear phenomena, end up producing a variety of novel patterns. We will briefly discuss some of these features, focusing on the case of (non)local minimal surfaces, (non)local phase coexistence models, and (non)local geometric flows.

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