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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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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DOI: https://doi.org/10.1007/s00032-013-0199-x