Hodge decomposition with degenerate weights and the Gross–Pitaevskii energy

We solve a Hodge decomposition problem with respect to a weight function that vanishes on the boundary. This problem is present in several works on the Gross–Pitaevskii energy, and we use our solution to show that a Γ -convergence result that links these works is still valid for more general data than previously considered. © 2007 Elsevier Inc. All rights reserved.