Branched microstructures: scaling and asymptotic self-similarity

摘要: We address some properties of a scalar two-dimensional model that has been proposed to describe microstructure in martensitic phase transformations, consisting minimizing the bulk energy where |uy| = 1 a.e. and u(0,·) 0. Kohn Muller [R. V. S. Muller, Comm. Pure Appl. Math.47 (1994), 405] proved existence minimizer for σ > 0 obtained bounds on total suggested self-similarity minimizer. Building upon their work, we derive local upper bound itself show u is asymptotically self-similar sense sequence (0 < θ 1) strongly converging subsequence W1,2. © 2000 John Wiley & Sons, Inc.