Singular perturbation of an elastic energy with a singular weight
2020
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 Muller (2001) we prove that a sequence of minimizers of the perturbed energies converges to a Young measure supported on piecewise-linear periodic functions of slope ± 1 whose period depends on the location in the domain and the weights in the energy.
Keywords:
- Correction
- Source
- Cite
- Save
- Machine Reading By IdeaReader
27
References
0
Citations
NaN
KQI