WIAS Preprint No. 2334, (2016)

Nonlocal phase transitions: Rigidity results and anisotropic geometry



Authors

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

2010 Mathematics Subject Classification

  • 35R11 60G22 82B26

Keywords

  • nonlocal phase transitions, rigidity results, sliding methods

DOI

10.20347/WIAS.PREPRINT.2334

Abstract

We provide a series of rigidity results for a nonlocal phase transition equation. The results that we obtain are an improvement of flatness theorem and a series of theorems concerning the one-dimensional symmetry for monotone and minimal solutions, in the research line dictaded by a classical conjecture of E. De Giorgi. Here, we collect a series of pivotal results, of geometric type, which are exploited in the proofs of the main results in a companion paper.

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