18 citations · 92 across the 40 of their papers we have counts for
5 papers · 1 filter
A Ginzburg-Landau model with topologically induced free discontinuities
Michael Goldman, Benoît Merlet, Vincent Millot
We study a variational model which combines features of the Ginzburg-Landau model in 2D and of the Mumford-Shah functional. As in the classical Ginzburg-Landau theory, a prescribed…
Equilibrium shapes of charged droplets and related problems: (mostly) a review
Michael Goldman, Berardo Ruffini
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either rest…
Self-similar minimizers of a branched transport functional
Michael Goldman
We solve here completely an irrigation problem from a Dirac mass to the Lebesgue measure. The functional we consider is a two dimensional analog of a functional previously derived…
A variational proof of partial regularity for optimal transportation maps
Michael Goldman, F Otto
We provide a new proof of the known partial regularity result for the optimal transportation map (Brenier map) between two sets. Contrary to the existing regularity theory for the…
A branched transport limit of the Ginzburg-Landau functional
Sergio Conti, Michael Goldman, Felix Otto +1
We study the Ginzburg-Landau model of type-I superconductors in the regime of small external magnetic fields. We show that, in an appropriate asymptotic regime, flux patterns are d…