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 Γ-convergence analysis, we show that as the parameter J converges to a critical value Jc, 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.

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

Runa E
2019-01-01

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 Γ-convergence analysis, we show that as the parameter J converges to a critical value Jc, 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.
Pattern formation, Nonlocal interactions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/26745
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