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We investigate minimizers defined on a bounded domain $\Omega$ in$\mathbb{R}^2$ for singular constrained energy functionals that include Balland Majumdar's modification of the Landau-de Gennes Q-tensor model for nematicliquid crystals. We prove regularity of minimizers with finite energy and showthat their range on compact subdomains of $\Omega$ does not intersect theboundary of the constraining set.

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