Analysis of microstructure of a non-convex functional with penalization term

We study the properties of the minimizers of a singularly perturbed non-convex functional with a penalization term , where I=(0,1), 0<ε≪1 and μ>0 are parameters, u is a given function and W(p)=2(p2−1). We analyze the phenomenon of microstructure formation and show the dependence on μ and u.