Sobolev spaces on metric measure spaces : an approach based on upper gradients / Juha Heinonen, Pekka Koskela, Nageswari Shanmugalingam, Jeremy T. Tyson.

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Analysis on metric spaces emerged in the 1990s as an independent research field providing a unified treatment of first-order analysis in diverse and potentially nonsmooth settings. Based on the fundamental concept of upper gradient, the notion of a Sobolev function was formulated in the setting of m...

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Bibliographic Details
Uniform Title:New mathematical monographs ; 27.
Main Authors: Heinonen, Juha (Author)
Koskela, Pekka (Author)
Shanmugalingam, Nageswari (Author)
Tyson, Jeremy T., 1972- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2015.
Series:New mathematical monographs ; 27.
Subjects:
Metric spaces.
Sobolev spaces.
Online Access:
Connect to online resource - MSU authorized users (Digital Object Identifier Permalink)
Physical Description:1 online resource (xii, 434 pages) : digital, PDF file(s).
Format: Electronic eBook
Contents:
  • Introduction
  • Review of basic functional analysis
  • Lebesgue theory of Banach space-valued functions
  • Lipschitz functions and embeddings
  • Path integrals and modulus
  • Upper gradients
  • Sobolev spaces
  • Poincaré inequalities
  • Consequences of Poincaré inequalities
  • Other definitions of Sobolev-type spaces
  • Gromov-Hausdorff convergence and Poincaré inequalities
  • Self-improvement of Poincaré inequalities
  • An introduction to Cheeger's differentiation theory
  • Examples, applications, and further research directions.