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arXiv · 1605.03794

Nonlocal phase transitions in homogeneous and periodic media

Matteo Cozzi·Serena Dipierro·Enrico Valdinoci
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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 $Γ$-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.

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Matteo Cozzi, Serena Dipierro, Enrico Valdinoci. 2016-05-12. Nonlocal phase transitions in homogeneous and periodic media. https://doi.org/10.1007/s11784-016-0359-z

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