Energyscaling, domain-branching and SO(2)-invariance in solid-solid phase transitions

In the early 90s Kohn and Müller established a model for the formation of domain pattern in martensitic shape-memory alloys. For a vectorial generalization of their model for solid-solid phase transitions with SO(2) invariance, we discuss the cases with one and two rank-1 connections and derive upper and lower bounds to the infimum energy with domain branching.