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arXiv · 1901.09940

Singular perturbation of an elastic energy with a singular weight

Oleksandr Misiats·Ihsan Topaloglu·Daniel Vasiliu
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Abstract

We study the singular perturbation of an elastic energy with a singular weight. The minimization of this energy results in a multi-scale pattern formation. We derive an energy scaling law in terms of the perturbation parameter and prove that, although one cannot expect periodicity of minimizers, the energy of a minimizer is uniformly distributed across the sample. Finally, following the approach developed by Alberti and M\"{u}ller in 2001 we prove that a sequence of minimizers of the perturbed energies converges to a Young measure supported on functions of slope $\pm 1$ and of period depending on the location in the domain and the weights in the energy.

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Oleksandr Misiats, Ihsan Topaloglu, Daniel Vasiliu. 2019-01-28. Singular perturbation of an elastic energy with a singular weight. https://doi.org/10.1016/j.physd.2020.132422

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