Geodesic
Weighted TV Minimization and Applications to Vortex Density Models
Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1051-1084
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Motivated by models arising in the description of Bose-Einstein condensation, we consider total variation minimization problems in which the total variation is weighted by a function that may degenerate near the domain boundary, and the fidelity term contains a weight that may be both degenerate and singular. We develop a general theory for a class of such problems, with special attention to the examples arising from physical models. 
@article{JCA_2017_24_4_JCA_2017_24_4_a0,
     author = {P. Athavale and R. L. Jerrard and M. Novaga and G. Orlandi},
     title = {Weighted {TV} {Minimization} and {Applications} to {Vortex} {Density} {Models}},
     journal = {Journal of convex analysis},
     pages = {1051--1084},
     year = {2017},
     volume = {24},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a0/}
}
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P. Athavale; R. L. Jerrard; M. Novaga; G. Orlandi. Weighted TV Minimization and Applications to Vortex Density Models. Journal of convex analysis, Tome 24 (2017) no. 4, pp. 1051-1084. http://geodesic.mathdoc.fr/item/JCA_2017_24_4_JCA_2017_24_4_a0/