WIAS Preprint No. 2345, (2016)

Improvement of flatness for nonlocal phase transitions


  • Dipierro, Serena
  • Serra, Joaquim
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R11 60G22 82B26


  • nonlocal phase transitions, rigidity results, sliding methods




We prove an improvement of flatness result for nonlocal phase transitions. For a class of nonlocal equations, we obtain a result in the same spirit of a celebrated theorem of Savin for the classical case. The results presented are completely new even for the case of the fractional Laplacian, but the robustness of the proofs allows us to treat also more general, possibly anisotropic, integro-differential operators.

Appeared in

  • Amer. J. Math., 142:4 (2020), pp. 1083-1160.

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