Abstract
In this chapter we review the definitions of Sobolev spaces, BV functions and perimeter of a set relative to the sub-Riemannian structure of ℍ. These notions are crucial for the development of sub-Riemannian geometric measure theory. Our treatment here is brief, focusing only on those aspects most relevant for the isoperimetric problem.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Birkhäuser Verlag AG
About this chapter
Cite this chapter
(2007). Sobolev and BV Spaces. In: Tyson, J.T. (eds) An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem. Progress in Mathematics, vol 259. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8133-2_5
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8133-2_5
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8132-5
Online ISBN: 978-3-7643-8133-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)