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Structure of stable solutions of a one-dimensional variational problem

2006
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E S A I M: Control, Optimisation and Calculus of Variations
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We prove the periodicity of all H 2 -local minimizers with low energy for a one-dimensional higher order variational problem. The results extend and complement an earlier work of Stefan Müller which concerns the structure of global minimizer. The energy functional studied in this work is motivated by the investigation of coherent solid phase transformations and the competition between the effects from regularization and formation of small scale structures. With a special choice of a bilinear

doi:10.1051/cocv:2006019
fatcat:cteiiwktqngg3nihqpqzbdqcui