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arXiv · 2409.16134

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

Janusz Ginster·Anastasija Pešić·Barbara Zwicknagl
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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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Janusz Ginster, Anastasija Pešić, Barbara Zwicknagl. 2024-09-24. Nonlinear interpolation inequalities with fractional Sobolev norms and pattern formation in biomembranes. https://arxiv.org/abs/2409.16134

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