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- W1966779513 abstract "We address some properties of a scalar two-dimensional model that has been proposed to describe microstructure in martensitic phase transformations, consisting of minimizing the bulk energy where |uy| = 1 a.e. and u(0,·) = 0. Kohn and Muller [R. V. Kohn and S. Muller, Comm. Pure and Appl. Math.47 (1994), 405] proved the existence of a minimizer for σ > 0 and obtained bounds on the total energy that suggested self-similarity of the minimizer. Building upon their work, we derive a local upper bound on the energy and on the minimizer itself and show that the minimizer u is asymptotically self-similar in the sense that the sequence (0 < θ < 1) has a strongly converging subsequence in W1,2. © 2000 John Wiley & Sons, Inc." @default.
- W1966779513 created "2016-06-24" @default.
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- W1966779513 date "2000-01-01" @default.
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- W1966779513 title "Branched microstructures: Scaling and asymptotic self-similarity" @default.
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- W1966779513 doi "https://doi.org/10.1002/1097-0312(200011)53:11<1448::aid-cpa6>3.0.co;2-c" @default.
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