A fractional framework for perimeters and phase transitions

TL;DR

This paper reviews recent findings on non-local perimeter minimisers related to phase coexistence models involving fractional Laplacian diffusion, highlighting advances in understanding phase transitions with fractional operators.

Contribution

It introduces a fractional framework for perimeters and phase transitions, connecting non-local geometric functionals with phase coexistence models.

Findings

Analysis of minimisers of non-local perimeter functionals

Connection between fractional Laplacian and phase coexistence

Insights into phase transition phenomena with fractional operators

Abstract

We review some recent results on minimisers of a non-local perimeter functional, in connection with some phase coexistence models whose diffusion term is given by the fractional Laplacian.