Γ-limit for a sharp interface model related to pattern formation on biomembranes - Brazke, Denis; Knüpfer, Hans; Marciniak-Czochra, Anna (Calculus of variations and partial differential equations, 2023)
We derive a macroscopic limit for a sharp interface version of a model proposed in Komura et al. (Langmuir 22:6771-6774, 2006) to investigate pattern formation due to competition of chemical and mechanical forces in biomembranes. We identify sub- and supercritical parameter regimes and show with the introduction of the autocorrelation function that the ground state energy leads to the isoperimetric problem in the subcritical regime, which is interpreted to not form fine scale patterns.