English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This thesis is devoted to the study of well-posedness properties of somegeometric variational problems: existence, regularity and uniqueness ofsolutions. We study two specific problems arising in the context of geometriccalculus of variations and sharing strong analogies: the Plateau's problem andthe optimal branched transport problem. The first part of the thesis discussesthe existence theory. Both problems are formulated in the language of Federerand Fleming's theory of currents. After an exposition of the main results, wewill present the core ideas of the (interior) regularity theory forarea-minimizing currents and for optimal transport paths. The last part of thethesis contains two original results: the generic uniqueness of solutions bothfor the Plateau's problem (in any dimension and codimension) and for theoptimal branched transport problem.

Well-posedness properties of geometric variational problems: existence, regularity and uniqueness results