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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
ADAMS, R.A.: Sobolev spaces. Pure and Applied Mathematics 65, Academic Press, New York — San Francisco — London, 1975.
GEHRING, F.W. and O. MARTIO: ‘Lipschitz classes and quasiconformal mappings’, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985), 203–219.
GEHRING, F.W. and B.S. OSGOOD: ‘Uniform domains and the quasihyperbolic metric’, J. Analyse Math. 36 (1979), 50–74.
KUFNER, A., O. JOHN, and S. FUCIK: Function spaces, Noordhoff International Publishing Leyden; Academia, Prague 1977.
LAPPALAINEN, V.: ‘Liph-extension domains’, Ann. Acad. Sci. Fenn. Ser. A I Math. Dissertationes 56 (1985).
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).
LAPPALAINEN, V. and A. LEHTONEN: ‘Embedding of Orlicz-Sobolew spaces in Hölder spaces’, Math. Scand. (to appear).
MANDELBROT, B.: The fractal geometry of nature, W.H. Freeman and Company, San Francisco 1982.
MARTIO, O.: ‘Definitions for uniform domains’, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 179–205.
NEČAS, J.: Les méthodes directes en théorie des équations elliptiques, Masson et Cie Editeurs, Paris; Academia, Editeurs, Prague 1967.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1989 Kluwer Academic Publishers
About this chapter
Cite this chapter
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
Download citation
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