Affiliations: Max Planck Institute for Mathematics in the Sciences, Inselstrasse 22-26, D-04103 Leipzig, Germany and Department of Mathematical Sciences, University of Bath, Bath BA2 7AY, UK. E-mail: N.Dirr@maths.bath.ac.uk | Mathematics Department, The City University of New York, CSI, Staten Island, NY 10314, USA. E-mail: mlucia@math.csi.cuny.edu | Dipartimento di Matematica, Università di Pisa, Largo B. Pontecorvo 5, 56127 Pisa, Italy. E-mail: novaga@dm.unipi.it
Note: [] Partially supported by DFG Research group 718: Analysis and Stochastics in Complex Physical Systems.
Note: [] Supported by an Alexander von Humboldt Fellowship.
Abstract: We consider the Γ-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 L2-topology.
