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Existence and partial regularity of static liquid crystal configurations. (English) Zbl 0611.35077

The object of the paper is the boundary problem of the liquid crystal static theory. Generally, the solution is a unit vector, minimizing the Oseen-Frank free energy.
The authors study the existence of the solution of its partial regularity and the conditions in which these properties hold, are shown. For the cholesteric liquid crystals in magnetic fields, also the existence and the partial regularity of the solution are studied in the smooth boundary conditions case.
Reviewer: Stefan Zanfir

MSC:

35Q82 PDEs in connection with statistical mechanics
35B65 Smoothness and regularity of solutions to PDEs
35D99 Generalized solutions to partial differential equations
82D25 Statistical mechanics of crystals
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