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arXiv · 1803.03850

Long-range phase coexistence models: recent progress on the fractional Allen-Cahn equation

Serena Dipierro·Enrico Valdinoci
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Abstract

In this set of notes, we present some recent developments on the fractional Allen-Cahn equation $$ (-\Delta)^s u = u-u^3,$$ with special attention to $\Gamma$-convergence results, energy and density estimates, convergence of level sets, Hamiltonian estimates, rigidity and symmetry results.

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Serena Dipierro, Enrico Valdinoci. 2018-03-10. Long-range phase coexistence models: recent progress on the fractional Allen-Cahn equation. https://arxiv.org/abs/1803.03850

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