Variational analysis of liquid crystals. (English) Zbl 07802844
Summary: This is an exposition of the role played by the calculus of variations in the field of liquid crystals, in particular the way it provides a sound foundation to the mathematical modelling and numerical study of their response to the confining material’s geometry and to external electromagnetic stimuli.
MSC:
| 49J53 | Set-valued and variational analysis |
| 35B36 | Pattern formations in context of PDEs |
| 49S05 | Variational principles of physics |
| 49J10 | Existence theories for free problems in two or more independent variables |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 49K10 | Optimality conditions for free problems in two or more independent variables |
| 49K20 | Optimality conditions for problems involving partial differential equations |
| 49K30 | Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.) |
| 49N60 | Regularity of solutions in optimal control |
| 82B21 | Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics |
| 82D30 | Statistical mechanics of random media, disordered materials (including liquid crystals and spin glasses) |
