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arXiv · 2307.01865

Phase separation on varying surfaces and convergence of diffuse interface approximations

Heiner Olbermann·Matthias Röger
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Abstract

In this paper we consider phase separations on (generalized) hypersurfaces in Euclidian space. We consider a diffuse surface area (line tension) energy of Modica-Mortola type and prove a compactness and lower bound estimate in the sharp interface limit. We use the concept of generalized BV functions over currents as introduced by Anzellotti et. al. [Annali di Matematica Pura ed Applicata, 170, 1996] to give a suitable formulation in the limit and achieve the necessary compactness property. We also consider an application to phase separated biomembranes where a Willmore energy for the membranes is combined with a generalized line tension energy. For a diffuse description of such energies we give a lower bound estimate in the sharp interface limit.

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Heiner Olbermann, Matthias Röger. 2023-07-04. Phase separation on varying surfaces and convergence of diffuse interface approximations. https://arxiv.org/abs/2307.01865

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