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SOBOLEV INEQUALITIES FOR ORLICZ SPACES OF TWO VARIABLE EXPONENTS

Published online by Cambridge University Press:  25 November 2009

PETER HÄSTÖ ,
YOSHIHIRO MIZUTA ,
TAKAO OHNO  and
TETSU SHIMOMURA
PETER HÄSTÖ
Affiliation:
Department of Mathematical Sciences, PO Box 3000, FI-90014, University of Oulu, Oulu, Finland e-mail: peter.hasto@helsinki.fi
YOSHIHIRO MIZUTA
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8521, Japan e-mail: yomizuta@hiroshima-u.ac.jp
TAKAO OHNO
Affiliation:
General Arts, Hiroshima National College of Maritime Technology, Higashino Oosakikamijima Toyotagun 725-0231, Japan e-mail: ohno@hiroshima-cmt.ac.jp
TETSU SHIMOMURA
Affiliation:
Department of Mathematics, Graduate School of Education, Hiroshima University, Higashi-Hiroshima 739-8524, Japan e-mail: tshimo@hiroshima-u.ac.jp
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Abstract

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Our aim in this paper is to deal with Sobolev's embeddings for Sobolev–Orlicz functions with ∇u ∈ Lp(·) logLq(·)(Ω) for Ω ⊂ n. Here p and q are variable exponents satisfying natural continuity conditions. Also the case when p attains the value 1 in some parts of the domain is included in the results.

Keywords

46E30
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 227 - 240
Copyright
Copyright © Glasgow Mathematical Journal Trust 2009

References

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