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A Fractional Framework for Perimeters and Phase Transitions

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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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano, Via Cesare Saldini 50, 20133, Milano, Italy

    Enrico Valdinoci

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  1. Enrico Valdinoci
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Correspondence to Enrico Valdinoci.

Additional information

I am greatly indebted to Begoña Barrios, Luis Caffarelli, Serena Dipierro, Alessio Figalli, Giampiero Palatucci, Ovidiu Savin and Yannick Sire: the results outlined in this note are the fruit of the very pleasant and stimulating collaboration with them and I profited enormously from the possibility of having them as mentors and coworkers. This work is supported by the ERC project \({\epsilon}\) (Elliptic Pde’s and Symmetry of Interfaces and Layers for Odd Nonlinearities) and the FIRB project A&B (Analysis and Beyond).

Lecture held in the Seminario Matematico e Fisico on Novemer 5, 2012.

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Valdinoci, E. A Fractional Framework for Perimeters and Phase Transitions. Milan J. Math. 81, 1–23 (2013). https://doi.org/10.1007/s00032-013-0199-x

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