  We consider the Landau-de Gennes variational problem on a bound\-ed, two
dimensional domain, subject to Dirichlet smooth boundary conditions. We prove
that minimizers are maximally biaxial near the singularities, that is, their
biaxiality parameter reaches the maximum value $1$. Moreover, we discuss the
convergence of minimizers in the vanishing elastic constant limit. Our
asymptotic analysis is performed in a general setting, which recovers the
Landau-de Gennes problem as a specific case.
