Preprint

Inserted: 21 jun 2024
Last Updated: 21 jun 2024

Year: 2024

Abstract:

In the present article we study diffuse interface models for two-phase biomembranes. We will do so by starting off with a diffuse interface model on Rn defined by two coupled phase fields $u, v$. The first phase field $u$ is the diffuse approximation of the interior of the membrane; the second phase field v is the diffuse approximation of the two phases of the membrane. We prove a compactness result and a lower bound in the sense of $\Gamma$-convergence for pairs of phase functions $(u_\epsilon, v_\epsilon)$. As an application of this first result, we consider a diffuse approximation of a two-phase Willmore functional plus line tension energy.

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