Journal of Convex Analysis 24 (2017), No. 4, 1051--1084
Copyright Heldermann Verlag 2017
Weighted TV Minimization and Applications to Vortex Density Models
Prashant Athavale
Dept. of Mathematics, University of Toronto, Toronto, Ont., Canada M5S 2E4
prashant@math.utoronto.ca
Robert L. Jerrard
Dept. of Mathematics, University of Toronto, Toronto, Ont., Canada M5S 2E4
rjerrard@math.toronto.edu
Matteo Novaga
Dip. di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy
matteo.novaga@unipi.it
Giandomenico Orlandi
Dip. di Informatica, Università di Verona, Verona, Italy
giandomenico.orlandi@univr.it
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.
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