Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models

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where F is quasiconvex in the gradient variables and the convex function f blows up to infinity at the boundary of a given bounded open set K ⊂ R . As we will explain later in Section 5, this sort of energy functional arises in some recently proposed models in nematic liquid crystal theory. We assume hereafter that U ⊂ R is bounded smooth domain and that K is a bounded, open convex subset of R. Our assumptions are these: (H1) Hypotheses on f : The given function f : R → [0,∞] is nonnegative, convex and smooth on K ⊂ R. We will write f = f(z). We further require that