Nonlocal phase transitions in homogeneous and periodic media
- Cozzi, Matteo
- Dipierro, Serena
- Valdinoci, Enrico
2010 Mathematics Subject Classification
- 35R11 82B26
- nonlocal Ginzburg-Landau-Allen-Cahn equation, De Giorgi conjecture, planelike minimizers, chaotic orbits
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.
- J. Fixed Point Theory Appl., 19:1 (2017) pp 387--405.