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

Revista Matemática Iberoamericana (2000)

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

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topShanmugalingam, 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 -

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