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A Variational Approach to Particles in Lipid Membranes

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Abstract

A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a variational framework, relate apparently different modelling approaches in terms of successive approximation, and investigate existence and uniqueness. Numerical computations illustrate that the new variational formulations are directly accessible to effective numerical methods.

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Authors and Affiliations

  1. Mathematics Institute, University of Warwick, Zeeman Building, Coventry, CV4 7AL, UK

    Charles M. Elliott & Graham Hobbs

  2. Institut für Mathematik, Freie Universität Berlin, Arnimallee 6, 14195, Berlin, Germany

    Carsten Gräser, Ralf Kornhuber & Maren-Wanda Wolf

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  1. Charles M. Elliott
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  2. Carsten Gräser
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  3. Graham Hobbs
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  4. Ralf Kornhuber
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  5. Maren-Wanda Wolf
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Correspondence to Ralf Kornhuber.

Additional information

Communicated by C. Le Bris

This work is partially supported by Freie Universität Berlin via the associated project AP01 of CRC 1114 funded by Deutsche Forschungsgemeinschaft (DFG). G.H. was supported by the UK Engineering and Physical Sciences Research Council (EPSRC) Grant EP/H023364/1 within the MASDOC Centre for Doctoral Training.

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Elliott, C.M., Gräser, C., Hobbs, G. et al. A Variational Approach to Particles in Lipid Membranes. Arch Rational Mech Anal 222, 1011–1075 (2016). https://doi.org/10.1007/s00205-016-1016-9

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