Data di Pubblicazione:
2017
Citazione:
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]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Chaotic orbits; De Giorgi conjecture; Nonlocal Ginzburg–Landau–Allen–Cahn equation; Planelike minimizers; Modeling and Simulation; Geometry and Topology; Applied Mathematics
Elenco autori:
M. Cozzi, S. Dipierro, E. Valdinoci
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