WIAS Preprint No. 3131, (2024)

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


Authors

  • Ginster, Janusz
    ORCID: 0000-0001-5825-1556
  • Pešić, Anastasija
  • Zwicknagl, Barbara
    ORCID: 0000-0002-6394-0775

2020 Mathematics Subject Classification

  • 46E35 47J20 49S05 74K15

Keywords

  • Scaling law, interpolation inequalities, fractional Sobolev norms, biomembranes, nonlocal energy, pattern formation

DOI

10.20347/WIAS.PREPRINT.3131

Abstract

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.

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