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

Nageswari Shanmugalingam

Revista Matemática Iberoamericana (2000)

  • Volume: 16, Issue: 2, page 243-279
  • ISSN: 0213-2230

Abstract

top
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.

How to cite

top

Shanmugalingam, Nageswari. "Newtonian spaces: An extension of Sobolev spaces to metric measure spaces.." Revista Matemática Iberoamericana 16.2 (2000): 243-279. <http://eudml.org/doc/39609>.

@article{Shanmugalingam2000,
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.},
author = {Shanmugalingam, Nageswari},
journal = {Revista Matemática Iberoamericana},
keywords = {Espacios de Sobolev; Espacios de Banach; Sobolev space; metric measure space; doubling space; gradient; Poincaré inequality; embedding theorem; capacity; path family},
language = {eng},
number = {2},
pages = {243-279},
title = {Newtonian spaces: An extension of Sobolev spaces to metric measure spaces.},
url = {http://eudml.org/doc/39609},
volume = {16},
year = {2000},
}

TY - JOUR
AU - Shanmugalingam, Nageswari
TI - Newtonian spaces: An extension of Sobolev spaces to metric measure spaces.
JO - Revista Matemática Iberoamericana
PY - 2000
VL - 16
IS - 2
SP - 243
EP - 279
AB - 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.
LA - eng
KW - Espacios de Sobolev; Espacios de Banach; Sobolev space; metric measure space; doubling space; gradient; Poincaré inequality; embedding theorem; capacity; path family
UR - http://eudml.org/doc/39609
ER -

Citations in EuDML Documents

top
  1. Marcello Lucia, Michael J. Puls, The p-Royden and p-Harmonic Boundaries for Metric Measure Spaces
  2. Nicola Gigli, An Overview of the Proof of the Splitting Theorem in Spaces with Non-Negative Ricci Curvature
  3. Anders Björn, Jana Björn, Approximations by regular sets and Wiener solutions in metric spaces
  4. Koskela, Pekka, Metric Sobolev spaces
  5. Guillaume Lupo-Krebs, Hervé Pajot, Dimensions conformes, espaces Gromov-hyperboliques et ensembles autosimilaires
  6. Zoltán M. Balogh, Jeremy T. Tyson, Kevin Wildrick, Dimension Distortion by Sobolev Mappings in Foliated Metric Spaces
  7. Zahra Sinaei, Riemannian Polyhedra and Liouville-Type Theorems for Harmonic Maps
  8. Nijjwal Karak, Generalized Lebesgue points for Sobolev functions
  9. H. Hakkarainen, R. Korte, P. Lahti, N. Shanmugalingam, Stability and Continuity of Functions of Least Gradient
  10. Kari Astala, Mario Bonk, Juha Heinonen, Quasiconformal mappings with Sobolev boundary values

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.