A nonlocal anisotropic model for phase transitions
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.
scientific article; zbMATH DE number 1143011