Nonlocal phase transitions in homogeneous and periodic media
  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. 
Matteo Cozzi, Serena Dipierro and Enrico Valdinoci
math.AP