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

Published online by Cambridge University Press:  21 July 2015

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.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2015 

References

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