Self-similar minimizers of a branched transport functional

Michael Goldman (1)

1 LJLL - Laboratoire Jacques-Louis Lions

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 in the study of branched patterns in type-I superconductors. The minimizer we obtain is a self-similar tree.

Domaines: Equations aux dérivées partielles [math.AP]

Michael Goldman. Self-similar minimizers of a branched transport functional. Indiana University Mathematics Journal, In press. ⟨hal-01505004v3⟩