A1 Journal article (refereed)
Variational problems concerning length distances in metric spaces (2024)

Essebei, F., & Pasqualetto, E. (2024). Variational problems concerning length distances in metric spaces. Journal of Mathematical Analysis and Applications, In Press. https://doi.org/10.1016/j.jmaa.2024.128337

JYU authors or editors

Publication details

All authors or editors: Essebei, Fares; Pasqualetto, Enrico

Journal or series: Journal of Mathematical Analysis and Applications

ISSN: 0022-247X

eISSN: 1096-0813

Publication year: 2024

Publication date: 24/03/2024

Volume: In Press

Publisher: Elsevier

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1016/j.jmaa.2024.128337

Publication open access: Openly available

Publication channel open access: Partially open access channel

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2305.02771

Abstract

Given a locally compact, complete metric space (X, D) and an open set Ω ⊆ X, we study the class of length distances d on Ω that are bounded from above and below by fixed multiples of the ambient distance D. More precisely, we prove that the uniform convergence on compact sets of distances in this class is equivalent to the Γ-convergence of several associated variational problems. Along the way, we fix some oversights appearing in the previous literature.

Keywords: calculus of variations; differential geometry; metric spaces

Free keywords: length distance; gamma-convergence; variational problem; length functional

Contributing organizations

Ministry reporting: Yes

Preliminary JUFO rating: 1