Phase separation on varying surfaces and convergence of diffuse interface approximations

Olbermann, Heiner;Röger, Matthias
(2023) Calculus of Variations and Partial Differential Equations — Vol. 62, n° 9, p. 250 (2023)

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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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Olbermann, H., & Röger, M. (2023). Phase separation on varying surfaces and convergence of diffuse interface approximations. Calculus of Variations and Partial Differential Equations, 62(9), 250. https://hdl.handle.net/2078.5/236505 (Original work published 2023)