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Embedding of Sobolev Spaces into Lipschitz Spaces

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Deformations of Mathematical Structures

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Abstract

The main result of the paper is that if Ω is a bounded uniform domain in ℝn and p>n, then the Sobolev space Wl, p(Ω) embeds continously into Cα(Ω̅), α = 1 - n/p.

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References

  1. ADAMS, R.A.: Sobolev spaces. Pure and Applied Mathematics 65, Academic Press, New York — San Francisco — London, 1975.

    MATH  Google Scholar 

  2. GEHRING, F.W. and O. MARTIO: ‘Lipschitz classes and quasiconformal mappings’, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203–219.

    MathSciNet  MATH  Google Scholar 

  3. GEHRING, F.W. and B.S. OSGOOD: ‘Uniform domains and the quasihyperbolic metric’, J. Analyse Math. 36 (1979), 50–74.

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  4. KUFNER, A., O. JOHN, and S. FUCIK: Function spaces, Noordhoff International Publishing Leyden; Academia, Prague 1977.

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  5. LAPPALAINEN, V.: ‘Liph-extension domains’, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 56 (1985).

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  6. LAPPALAINEN, V.: Local and Global Lipschitz Classes, Seminar on Deformations, Łódź-Lublin 1985/87, ed. by J. Ławrynowicz, D. Reidel Publishing Company, Dordrecht (to appear).

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  7. LAPPALAINEN, V. and A. LEHTONEN: ‘Embedding of Orlicz-Sobolew spaces in Hölder spaces’, Math. Scand. (to appear).

    Google Scholar 

  8. MANDELBROT, B.: The fractal geometry of nature, W.H. Freeman and Company, San Francisco 1982.

    MATH  Google Scholar 

  9. MARTIO, O.: ‘Definitions for uniform domains’, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 179–205.

    MathSciNet  Google Scholar 

  10. NEČAS, J.: Les méthodes directes en théorie des équations elliptiques, Masson et Cie Editeurs, Paris; Academia, Editeurs, Prague 1967.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Jyva̎skyla̎, SF-40100, Jyva̎skyla̎, Finland

    Ari Lehtonen

Authors
  1. Ari Lehtonen
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Editor information

Editors and Affiliations

  1. Institute of Mathematics of the Polish Academy of Sciences, Łódź, Poland

    Julian Ławrynowicz

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© 1989 Kluwer Academic Publishers

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Lehtonen, A. (1989). Embedding of Sobolev Spaces into Lipschitz Spaces. In: Ławrynowicz, J. (eds) Deformations of Mathematical Structures. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2643-1_2

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  • DOI: https://doi.org/10.1007/978-94-009-2643-1_2

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-7693-7

  • Online ISBN: 978-94-009-2643-1

  • eBook Packages: Springer Book Archive

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