We prove the periodicity of all H 2-local minimizers with low energyfor a one-dimensional higher order variational problem.The results extend and complement an earlier work of Stefan Müllerwhich concerns the structure of global minimizer.The energy functional studied in this work is motivated by theinvestigation of coherent solid phase transformations and thecompetition between theeffects from regularization and formation of small scale structures.With a special choice of a bilinear double well potential function, wemake use of explicit solution formulas to analyze the intricateinteractions between the phase boundaries. Our analysis can provideinsights for tackling the problem with general potential functions.
