Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Introduction Read chapter Read first chapter

2019 | OriginalPaper | Chapter

6. Sobolev Spaces

Authors : Petteri Harjulehto, Peter Hästö

Published in: Orlicz Spaces and Generalized Orlicz Spaces

Publisher: Springer International Publishing

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this chapter we study Sobolev spaces with generalized Orlicz integrability. We point out the novelties in this new setting and assume that the readers are familiar with classical Sobolev spaces.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

inform now
previous chapter Extrapolation and Interpolation
next chapter Special Cases
Literature
2.
R. Adams. Sobolev Spaces. Pure and Applied Mathematics, Vol. 65 (Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London, 1975)
3.
R. Adams, J. Fournier, Sobolev Spaces, volume 140 of Pure and Applied Mathematics (Amsterdam), 2nd edn. (Elsevier/Academic Press, Amsterdam, 2003)
12.
B. Bojarski, Remarks on Sobolev imbedding inequalities, in Complex Analysis, Joensuu 1987, volume 1351 of Lecture Notes in Math. (Springer, Berlin, 1988), pp. 52–68
27.
D. Cruz-Uribe, A. Fiorenza, Variable Lebesgue Spaces: Foundations and Harmonic Analysis (Birkhäuser, Basel, 2013)CrossRef
30.
D. Cruz-Uribe, J.M. Martell, C. Pérez, Weights, Extrapolation and the Theory of Rubio de Francia, volume 215 of Operator Theory: Advances and Applications (Birkhäuser/Springer Basel AG, Basel, 2011)
34.
L. Diening, P. Harjulehto, P. Hästö, M. Růžička, Lebesgue and Sobolev spaces with Variable Exponents, volume 2017 of Lecture Notes in Mathematics (Springer, Heidelberg, 2011)MATH
36.
L. Diening, S. Schwarzacher, Global gradient estimates for the p(⋅)-Laplacian. Nonlinear Anal. 106, 70–85 (2014)MathSciNetCrossRef
46.
D. Gilbarg, N. Trudinger, Elliptic Partial Differential Equations of Second Order. Classics in Mathematics (Springer, Berlin, 2001). Reprint of the 1998 editionMATH
63.
J. Heinonen, T. Kilpeläinen, O. Martio, Nonlinear Potential Theory of Degenerate Elliptic Equations (Dover Publications, Mineola, NY, 2006). Unabridged republication of the 1993 original
88.
J. Malý, W.P. Ziemer, Fine Regularity of Solutions of Elliptic Partial Differential Equations, volume 51 of Mathematical Surveys and Monographs (American Mathematical Society, Providence, RI, 1997)CrossRef
118.
Y.G. Reshetnyak, Integral representations of differentiable functions in domains with a nonsmooth boundary. Sibirsk. Mat. Zh. 21(6), 108–116, 221 (1980)MathSciNetCrossRef
131.
W. Ziemer, Weakly Differentiable Functions, volume 120 of Graduate Texts in Mathematics (Springer, New York, 1989). Sobolev spaces and functions of bounded variation
Metadata
Title
Sobolev Spaces
Authors
Petteri Harjulehto
Peter Hästö
Copyright Year
2019
Book
Orlicz Spaces and Generalized Orlicz Spaces

Print ISBN: 978-3-030-15099-0

Electronic ISBN: 978-3-030-15100-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-15100-3_6

Premium Partner

    Image Credits