Calculus of Variations and Geometric Measure Theory
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M. Goldman - E. Runa

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

created by goldman on 22 Nov 2016
modified on 21 Aug 2017

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Submitted Paper

Inserted: 22 nov 2016
Last Updated: 21 aug 2017

Year: 2016

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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