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Motivated in part by models arising from mathematical descriptions ofBose-Einstein condensation, we consider total variation minimization problemsin which the total variation is weighted by a function that may degenerate nearthe domain boundary, and the fidelity term contains a weight that may be bothdegenerate and singular. We develop a general theory for a class of suchproblems, with special attention to the examples arising from physical models.

Weighted TV minimization and applications to vortex density models