Calculus of Variations and Geometric Measure Theory

N. Dirr - M. Lucia - M. Novaga

Gradient theory of phase transitions with a rapidly oscillating forcing term

created by novaga on 03 Oct 2007
modified on 10 Nov 2018


Published Paper

Inserted: 3 oct 2007
Last Updated: 10 nov 2018

Journal: Asymptotic Analysis
Volume: 60
Pages: 29-59
Year: 2008


We consider the Gamma-limit of a family of functionals which model the interaction of a material that undergoes phase transition with a rapidly oscillating conservative vector field. These functionals consist of a gradient term, a double-well potential and a vector field. The scaling is such that all three terms scale in the same way and the frequency of the vector field is equal to the interface thickness. Difficulties arise from the fact that the two global minimizers of the functionals are nonconstant and converge only in the weak $L^2$-topology.