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