Long-range Phase Coexistence Models: Recent Progress on the Fractional Allen-Cahn Equation

  • Serena DipierroEmail author
  • Enrico Valdinoci
Conference paper
Part of the CIM Series in Mathematical Sciences book series (CIMSMS)


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


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and Statistics, University of Western AustraliaCrawley WAAustralia

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