Small deformations of Helfrich energy minimising surfaces with applications to biomembranes

DOI10.1142/S0218202517500269zbMath1368.74039arXiv1610.05240MaRDI QIDQ4977913

Charles M. Elliott, Graham Hobbs, Hans Fritz

Publication date: 17 August 2017

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1610.05240

zbMATH Keywords

point forcesdiscretisationHelfrich energyexistence and uniqueness of weak solutionsPDEs on surfacessurface finite element methodsurface deformations

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Biomechanical solid mechanics (74L15) Applications of PDEs on manifolds (58J90) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (12)

A formula for membrane mediated point particle interactions on near spherical biomembranes ⋮ Connected surfaces with boundary minimizing the Willmore energy ⋮ On the sharp interface limit of a phase field model for near spherical two phase biomembranes ⋮ Stationary surfaces with boundaries ⋮ On the variation of curvature functionals in a space form with application to a generalized Willmore energy ⋮ Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves ⋮ Second order splitting of a class of fourth order PDEs with point constraints ⋮ Mini-workshop: PDE models of motility and invasion in active biosystems. Abstracts from the mini-workshop held October 22--28, 2017 ⋮ Small deformations of spherical biomembranes ⋮ Second order splitting for a class of fourth order equations ⋮ On differentiability of the membrane-mediated mechanical interaction energy of discrete-continuum membrane-particle models ⋮ Domain formation via phase separation for spherical biomembranes with small deformations

Cites Work

• A variational approach to particles in lipid membranes
• Local minimizers of the Willmore functional
• A gap theorem for Willmore tori and an application to the Willmore flow
• Computation of geometric partial differential equations and mean curvature flow
• The Jordan-Brouwer Separation Theorem for Smooth Hypersurfaces
• A Second Order Shape Optimization Approach for Image Segmentation
• Finite element methods for surface PDEs
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