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On density of smooth functions in weighted Sobolev spaces with variable exponents

Authors: V. V. Zhikov and M. D. Surnachev
Translated by: N. Rastegaev
Original publication: Algebra i Analiz, tom 27 (2015), nomer 3.
Journal: St. Petersburg Math. J. 27 (2016), 415-436
MSC (2010): Primary 46E35
Published electronically: March 30, 2016
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Abstract: A sufficient condition for the density of smooth functions in the weighted Sobolev space with variable exponent is obtained. This condition is formulated in terms of the asymptotic behavior of the integrals of negative and positive powers of the weight.

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Additional Information

V. V. Zhikov
Affiliation: Vladimir State University, Stroitelei Ave., 600000 Vladimir, Russia

M. D. Surnachev
Affiliation: Aeroacustics Laboratory, Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, 4 Miusskaya square, 125047 Moscow, Russia

Keywords: Density of smooth functions, Lavrentiev phenomenon, Sobolev--Orlicz spaces, variable exponent, Muckenhoupt classes.
Received by editor(s): September 15, 2014
Published electronically: March 30, 2016
Additional Notes: Supported by RFBR (projects nos. 14-01-31341 and 14-01-00192). The results of §4 were obtained with the support of Russian Science Foundation (project no. 14-11-00398).
Dedicated: Dedicated to Nina Ural’tseva on the occasion of her anniversary.
Article copyright: © Copyright 2016 American Mathematical Society