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