Nonlocal phase transitions in homogeneous and periodic media
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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 GG -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.
CitationCozzi, M., Dipierro, S., Valdinoci, E. Nonlocal phase transitions in homogeneous and periodic media. "Journal of fixed point theory and applications", 1 Març 2017, vol. 19, núm. 1, p. 387-405.