A varifold perspective on the $p$-elastic energy of planar sets
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Publication:3303380
zbMath1446.49032arXiv1902.10463MaRDI QIDQ3303380
Publication date: 11 August 2020
Full work available at URL: https://arxiv.org/abs/1902.10463
Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Variational problems in a geometric measure-theoretic setting (49Q20) Methods involving semicontinuity and convergence; relaxation (49J45) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Optimization of shapes other than minimal surfaces (49Q10)
Related Items (7)
The Łojasiewicz-Simon inequality for the elastic flow ⋮ A relation between cylindrical critical points of Willmore-type energies, weighted areas and vertical potential energies ⋮ A Li-Yau inequality for the 1-dimensional Willmore energy ⋮ Boundary value problems for a special Helfrich functional for surfaces of revolution: existence and asymptotic behaviour ⋮ Elastic networks, statics and dynamics ⋮ A survey of the elastic flow of curves and networks ⋮ Degenerate elastic networks
Cites Work
- Implicit time discretization for the mean curvature flow equation
- A direct variational approach to a problem arising in image reconstruction
- Characterization and representation of the lower semicontinuous envelope of the elastica functional
- Existence of surfaces minimizing the Willmore functional
- Weakly differentiable functions on varifolds
- A coarea-type formula for the relaxation of a generalized elastica functional
- Gradient Young measures, varifolds, and a generalized Willmore functional
- Minimal elastic networks
- Locality of the mean curvature of rectifiable varifolds
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