Journal article
About Sobolev spaces on fractals: fractal gradians and Laplacians
Aequationes mathematicae, Vol.99(2), pp.465-490
04/2025
DOI: 10.1007/s00010-024-01060-6
Abstract
The paper covers the foundations of fractal calculus on fractal curves, defines different function classes, establishes vector spaces for F alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F<^>{\alpha }$$\end{document}-integrable functions, introduces local fractal integrable functions and fractal distribution functionals, defines the dual space of a fractal function space, proves completeness for F alpha\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F<^>{\alpha }$$\end{document}-differentiable function spaces, defines Fractal Sobolev spaces, and introduces fractal gradian and fractal Laplace operators on fractal Hilbert spaces. It also presents criteria for the existence of unique solutions to fractal differential equations.
Details
- Title: Subtitle
- About Sobolev spaces on fractals: fractal gradians and Laplacians
- Creators
- Alireza Khalili Golmankhaneh - Islamic Azad University of UrmiaPalle E. T. Jorgensen - Univ Iowa, Dept Math, Iowa City, IA 52242 USACristina Serpa - Instituto Politécnico de LisboaKerri Welch - California Institute of Integral Studies
- Resource Type
- Journal article
- Publication Details
- Aequationes mathematicae, Vol.99(2), pp.465-490
- DOI
- 10.1007/s00010-024-01060-6
- ISSN
- 0001-9054
- eISSN
- 1420-8903
- Publisher
- Springer Nature
- Number of pages
- 26
- Grant note
- UIDB/04561/2020 / Portuguese National Funding from FCT-Fundacao para a Ciencia e a Tecnologia
- Language
- English
- Electronic publication date
- 04/16/2024
- Date published
- 04/2025
- Academic Unit
- Mathematics
- Record Identifier
- 9984619460202771
Metrics
33 Record Views