JournalsrmiVol. 16, No. 2pp. 243–279

Newtonian spaces: An extension of Sobolev spaces to metric measure spaces

  • Nageswari Shanmugalingam

    University of Cincinnati, USA
Newtonian spaces: An extension of Sobolev spaces to metric measure spaces cover
Download PDF

Abstract

This paper studies a possible definition of Sobolev spaces in abstract metric spaces and answers in the affirmative the question whether this definition yields a Banach space. The paper also explores the relationship between this definition and the Hajlasz spaces. For specialized metric spaces the Sobolev embedding theorems are proven. Different versions of capacities are also explored and these various definitions are compared. The main tool used in this paper is the concept of moduli of path families.

Cite this article

Nageswari Shanmugalingam, Newtonian spaces: An extension of Sobolev spaces to metric measure spaces. Rev. Mat. Iberoam. 16 (2000), no. 2, pp. 243–279

DOI 10.4171/RMI/275