On the optimality of stripes in a variational model with non-local interactions

Michael Goldman; Eris Runa

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arXiv · 1611.07228

On the optimality of stripes in a variational model with non-local interactions

Michael Goldman·Eris Runa

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Abstract

We study pattern formation for a variational model displaying competition between a local term penalizing interfaces and a non-local term favoring oscillations. By means of a $\Gamma$--convergence analysis, we show that as the parameter J converges to a critical value J c, the minimizers converge to periodic one-dimensional stripes. A similar analysis has been previously performed by other authors for related discrete systems. In that context, a central point is that each " angle " comes with a strictly positive contribution to the energy. Since this is not anymore the case in the continuous setting, we need to overcome this difficulty by slicing arguments and a rigidity result.

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Michael Goldman, Eris Runa. 2016-11-22. On the optimality of stripes in a variational model with non-local interactions. https://arxiv.org/abs/1611.07228

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