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EMBEDDING AND TRACE RESULTS FOR VARIABLE EXPONENT SOBOLEV AND MAZ'YA SPACES ON NON-SMOOTH DOMAINS

Part of: General theory of linear operators Special classes of linear operators Elliptic equations and systems

Published online by Cambridge University Press:  21 July 2015

ALEJANDRO VÉLEZ-SANTIAGO
ALEJANDRO VÉLEZ-SANTIAGO*
Affiliation:
Department of Mathematics, University of California, Riverside, CA 92521-0135, USA e-mail: avelez@math.ucr.edu, alejandro.velez2@upr.edu, alejovelez32@gmail.com
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Abstract

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We establish interior and trace embedding results for Sobolev functions on a class of bounded non-smooth domains. Also, we define the corresponding generalized Maz'ya spaces of variable exponent, and obtain embedding results similar as in the constant case. Some relations between the variable exponent Maz'ya spaces and the variable exponent Sobolev spaces are also achieved. At the end, we give an application of the previous results for the well-posedness of a class of quasi-linear equations with variable exponent.

MSC classification

Primary: 47A63: Operator inequalities
Secondary: 47B38: Operators on function spaces (general) 47A07: Forms (bilinear, sesquilinear, multilinear) 35J92: Quasilinear elliptic equations with $p$-Laplacian

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 58 , Issue 2 , May 2016 , pp. 471 - 489
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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