Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions

Geng, Zhiyuan; Tong, Jianliang

doi:10.1007/s00526-020-1717-7

Cited by 7 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such minimizers are called "physically realistic." Additional features for minimizers, Q of I LdG with Ω in R 3 were obtained by Geng and Tong in [8]. In particular, assuming specific conditions on G(Q, DQ) they proved higher integrability properties for |D Q|.…”

mentioning

confidence: 85%

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Bauman¹,

Phillips²

2021

Preprint

View full text Add to dashboard Cite

We investigate minimizers defined on a bounded domain Ω in R 2 for singular constrained energy functionals that include Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model for nematic liquid crystals. We prove regularity of minimizers with finite energy and show that their range on compact subdomains of Ω does not intersect the boundary of the constraining set. We apply this result to prove that minimizers of the constrained Landau-de Gennes Q-tensor energy for liquid crystals composed of a singular Maier-Saupe bulk term and all elasticity terms with coefficients L 1 , • • • , L 5 , are C 2 in Ω; and their eigenvalues on compact subsets of Ω are contained in closed subintervals of the physical range (− 1 3 , 2 3 ).

show abstract

mentioning

confidence: 85%

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Bauman¹,

Phillips²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…Meanwhile, various problems in static and dynamic configurations concerning ψ can be found in [7,12,[14][15][16][17]29]. Specifically, the free energy in related dynamic problems considered so far in the existing literature [12,15,16,29] only involves the L 1 isotropic term.…”

Section: Introductionmentioning

confidence: 99%

Regularity of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential

Liu¹,

Lu²,

Xu³

2020

Preprint

View full text Add to dashboard Cite

In this paper we study a gradient flow generated by the Landau-de Gennes free energy that describes nematic liquid crystal configurations in the space of Q-tensors. This free energy density functional is composed of three quadratic terms as the elastic energy density part, and a singular potential in the bulk part that is considered as a natural enforcement of a physical constraint on the eigenvalues of Q. The system is a non-diagonal parabolic system with a singular potential which trends to infinity logarithmically when the eigenvalues of Q approaches the physical boundary. We give a rigorous proof that for rather general initial data with possibly infinite free energy, the system has a unique strong solution after any positive time t 0 . Furthermore, this unique strong solution detaches from the physical boundary after a sufficiently large time T 0 . We also give estimate of the Hausdorff measure of the set where the solution touches the physical boundary and thus prove a partial regularity result of the solution in the intermediate stage (0, T 0 ).

show abstract

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Bauman

Phillips

2022

Association for Women in Mathematics Series

View full text Add to dashboard Cite

Regularity of minimizers of a tensor-valued variational obstacle problem in three dimensions

Cited by 7 publications

References 12 publications

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Regularity of a gradient flow generated by the anisotropic Landau-de Gennes energy with a singular potential

Regularity of Minimizers for a General Class of Constrained Energies in Two-Dimensional Domains with Applications to Liquid Crystals

Contact Info

Product

Resources

About