Energy minimizing maps with prescribed singularities and Gilbert-Steiner optimal networks

Autor:	Sisto Baldo, Van Phu Cuong Le, Annalisa Massaccesi, Giandomenico Orlandi
Jazyk:	angličtina
Rok vydání:	2023
Předmět:	liquid crystals optimal mappings steiner tree problem branched optimal transport homological plateau problem $ g $-currents Applied mathematics. Quantitative methods T57-57.97
Zdroj:	Mathematics in Engineering, Vol 5, Iss 4, Pp 1-19 (2023)
Druh dokumentu:	article
ISSN:	2640-3501 89488695
DOI:	10.3934/mine.2023078?viewType=HTML
Popis:	We investigate the relation between energy minimizing maps valued into spheres having topological singularities at given points and optimal networks connecting them (e.g., Steiner trees, Gilbert-Steiner irrigation networks). We show the equivalence of the corresponding variational problems, interpreting in particular the branched optimal transport problem as a homological Plateau problem for rectifiable currents with values in a suitable normed group. This generalizes the pioneering work by Brezis, Coron and Lieb [10].
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/2b9a1e3daf89488695bce9905e752234 Zobrazit plný text záznamu View record in DOAJ