A nonlocal anisotropic model for phase transitions
type: Item
instance of: scholarly article
title: A nonlocal anisotropic model for phase transitions
zbMATH Open document ID: 0891.49021
author: Giovanni Alberti
author: Giovanni Bellettini
published in: Mathematische Annalen
publication date: 1998-04-20T00:00:00Z
review text: We study the one- and \(N\)-dimensional optimal profiles for the interface in a nonlocal model for phase transitions described by the free energy \[ F(u):= \textstyle{{1\over 4}} \int\int J(x'- x)(u(x')- u(x))^2 dx'dx+ \int W(u(x))dx, \] where \(u\) is a scalar density function, \(W\) is a double-well potential, and \(J\) is a positive anisotropic interaction potential.
Mathematics Subject Classification ID: 49N45
Mathematics Subject Classification ID: 82B24
Mathematics Subject Classification ID: 47J05
Mathematics Subject Classification ID: 49J45
zbMATH DE Number: 1143011
zbMATH Keywords: interface optimal profile
zbMATH Keywords: nonlocal integral functionals
zbMATH Keywords: increasing rearrangement
zbMATH Keywords: phase transitions
MaRDI profile type: Publication
full work available at URL: s002080050159
OpenAlex ID: W2066600510
DOI: 10.1007/S002080050159
description: scientific article; zbMATH DE number 1143011