Existence of varifold minimizers for the multiphase Canham-Helfrich functional

DOI10.1007/s00526-020-01759-9zbMath1439.49074arXiv1912.02614OpenAlexW3021004139MaRDI QIDQ2180859

Luca Lussardi, Ulisse Stefanelli, Katharina Brazda

Publication date: 15 May 2020

Published in: Calculus of Variations and Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1912.02614

zbMATH Keywords

lower semicontinuitybiological membranesCanham-Helfrich functionalcurvature varifolds

Mathematics Subject Classification ID

Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Biomechanics (92C10) Applications of global differential geometry to the sciences (53C80) Optimization of shapes other than minimal surfaces (49Q10)

Related Items (9)

On the sharp interface limit of a phase field model for near spherical two phase biomembranes ⋮ Embedded Delaunay tori and their Willmore energy ⋮ Phase separation on varying surfaces and convergence of diffuse interface approximations ⋮ Li-Yau inequalities for the Helfrich functional and applications ⋮ Variational models for the interaction of surfactants with curvature – existence and regularity of minimizers in the case of flexible curves ⋮ Numerical shape optimization of the Canham-Helfrich-Evans bending energy ⋮ Direct minimization of the Canham-Helfrich energy on generalized Gauss graphs ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ Minimisers of Helfrich functional for surfaces of revolution

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