Nonlocal phase transitions in homogeneous and periodic media

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...

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Detalles Bibliográficos
Autores: Cozzi, Matteo|||0000-0001-6105-692X, Dipierro, Serena, Valdinoci, Enrico
Tipo de recurso: artículo
Fecha de publicación:2017
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/104173
Acceso en línea:https://hdl.handle.net/2117/104173
https://dx.doi.org/10.1007/s11784-016-0359-z
Access Level:acceso abierto
Palabra clave:Chaotic behavior in systems
Nonlocal Ginzburg-Landau-Allen-Cahn equation
De Giorgi conjecture
Planelike minimizers
Chaotic orbits
Càlcul de variacions
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Càlcul de variacions
Descripción
Sumario: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.