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<p>We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling laws for the minimal energy. As a main tool we present new nonlinear interpolation inequalities that bound fractional Sobolev seminorms in terms of a Cahn-Hillard/Modica-Mortola energy.</p>

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Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年1月12日

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  • J. Ginster,
  • A. Pešić,
  • B. Zwicknagl

摘要

We consider a one-dimensional version of a variational model for pattern formation in biological membranes. The driving term in the energy is a coupling between the order parameter and the local curvature of the membrane. We derive scaling laws for the minimal energy. As a main tool we present new nonlinear interpolation inequalities that bound fractional Sobolev seminorms in terms of a Cahn-Hillard/Modica-Mortola energy.