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.

Nonlocal phase transitions in homogeneous and periodic media / M. Cozzi, S. Dipierro, E. Valdinoci. - In: JOURNAL OF FIXED POINT THEORY AND ITS APPLICATIONS. - ISSN 1661-7738. - 19:1(2017), pp. 387-405. [10.1007/s11784-016-0359-z]

Nonlocal phase transitions in homogeneous and periodic media

M. Cozzi
Primo
;
S. Dipierro;E. Valdinoci
Ultimo
2017

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.
Chaotic orbits; De Giorgi conjecture; Nonlocal Ginzburg–Landau–Allen–Cahn equation; Planelike minimizers; Modeling and Simulation; Geometry and Topology; Applied Mathematics
Settore MAT/05 - Analisi Matematica
2017
http://www.springer.com/west/home?SGWID=4-102-70-173671503-0&changeHeader=true
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/488657
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