Proceedings of the Japan Academy, Series A, Mathematical Sciences

Continuity of Sobolev functions of variable exponent on metric spaces

Yoshihiro Mizuta and Tetsu Shimomura

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Abstract

Our aim in this paper is to discuss continuity of Sobolev functions of variable exponent on metric spaces in the limiting case of Sobolev's imbedding theorem.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 80, Number 6 (2004), 96-99.

Dates
First available in Project Euclid: 13 May 2005

Permanent link to this document
https://projecteuclid.org/euclid.pja/1116014784

Digital Object Identifier
doi:10.3792/pjaa.80.96

Mathematical Reviews number (MathSciNet)
MR2075449

Zentralblatt MATH identifier
1072.46506

Subjects
Primary: 46E35: Sobolev spaces and other spaces of "smooth" functions, embedding theorems, trace theorems

Keywords
Hölder continuity differentiability weighted Sobolev spaces $A_p$-weight $p$-Poincaré inequality Sobolev's imbedding theorem of variable exponent

Citation

Mizuta, Yoshihiro; Shimomura, Tetsu. Continuity of Sobolev functions of variable exponent on metric spaces. Proc. Japan Acad. Ser. A Math. Sci. 80 (2004), no. 6, 96--99. doi:10.3792/pjaa.80.96. https://projecteuclid.org/euclid.pja/1116014784


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