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

Zhikov, V.; Surnachev, M.

doi:10.1090/spmj/1396

On density of smooth functions in weighted Sobolev spaces with variable exponents
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by V. V. Zhikov and M. D. Surnachev
Translated by: N. Rastegaev

St. Petersburg Math. J. 27 (2016), 415-436

DOI: https://doi.org/10.1090/spmj/1396

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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