  This paper is concerned with eigenvalue problems for non-symmetric elliptic
operators with large drifts in bounded domains under Dirichlet boundary
conditions. We consider the minimal principal eigenvalue and the related
principal eigenfunction in the class of drifts having a given, but large,
pointwise upper bound. We show that, in the asymptotic limit of large drifts,
the maximal points of the optimal principal eigenfunctions converge to the set
of points maximizing the distance to the boundary of the domain. We also show
the uniform asymptotic profile of these principal eigenfunctions and the
direction of their gradients in neighborhoods of the boundary.
