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We study the ground state which minimizes a Gross-Pitaevskii energy withgeneral non-radial trapping potential, under the unit mass constraint, in theThomas-Fermi limit where a small parameter tends to 0. This ground state playsan important role in the mathematical treatment of recent experiments on thephenomenon of Bose-Einstein condensation, and in the study of various types ofsolutions of nonhomogeneous defocusing nonlinear Schrodinger equations. Many ofthese applications require delicate estimates for the behavior of the groundstate near the boundary of the condensate, as the singular parameter tends tozero, in the vicinity of which the ground state has irregular behavior in theform of a steep corner layer. In particular, the role of this layer isimportant in order to detect the presence of vortices in the small densityregion of the condensate, understand the superfluid flow around an obstacle,and also has a leading order contribution in the energy. In contrast toprevious approaches, we utilize a perturbation argument to go beyond theclassical Thomas-Fermi approximation and accurately approximate the layer bythe Hastings-McLeod solution of the Painleve-II equation. This settles an openproblem, answered very recently only for the special case of the model harmonicpotential. In fact, we even improve upon previous results that relied heavilyon the radial symmetry of the potential trap. Moreover, we show that the groundstate has the maximal regularity available, namely it remains uniformly boundedin the 1/2-Holder norm, which is the exact Holder regularity of the singularlimit profile, as the singular parameter tends to zero. Our study is highlymotivated by an interesting open problem posed recently by Aftalion, Jerrard,and Royo-Letelier, and an open question of Gallo and Pelinovsky, concerning theremoval of the radial symmetry assumption from the potential trap.

The ground state of a Gross-Pitaevskii energy with general potential in the Thomas-Fermi limit