WIAS Preprint No. 2262, (2016)

Nonlocal phase transitions in homogeneous and periodic media


Authors

  • Cozzi, Matteo
  • Dipierro, Serena
  • Valdinoci, Enrico
    ORCID: 0000-0001-6222-2272

2010 Mathematics Subject Classification

  • 35R11 82B26

Keywords

  • nonlocal Ginzburg-Landau-Allen-Cahn equation, De Giorgi conjecture, planelike minimizers, chaotic orbits

DOI

10.20347/WIAS.PREPRINT.2262

Abstract

We discuss some results related to a phase transition model in which the potential energy induced by a double-well function is balanced by a fractional elastic energy. In particular, we present asymptotic results (such as Gamma-convergence, energy bounds and density estimates for level sets), flatness and rigidity results, and the construction of planelike minimizers in periodic media.
Finally, we consider a nonlocal equation with a multiwell potential, motivated by models arising in crystal dislocations, and we construct orbits exhibiting symbolic dynamics, inspired by some classical results by Paul Rabinowitz.

Appeared in

  • J. Fixed Point Theory Appl., 19:1 (2017) pp 387--405.

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