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Mat. Sb., 2000, Volume 191, Number 2, Pages 132–148 (Mi msb455)  

This article is cited in 2 scientific papers (total in 2 papers)

Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the space $L_p(\Omega;\omega)$

L. K. Kusainova

Institute of Applied Mathematics National Academy of Sciences of Kazakhstan

Abstract: Several conditions on the weight functions $v$ and $\omega$ are obtained that guarantee the embedding inequality
$$ \|u\|_{L_p(\Omega;\omega)}\leqslant C[(\int_\Omega|\nabla_lu|^p)^{1/p}+(\int_\Omega|u|^pv)^{1/p}], \qquad 1<p<n/l. $$
Classes of weights $\omega$ and $v$ in which these conditions are both necessary and sufficient are described.

DOI: https://doi.org/10.4213/sm455

Full text: PDF file (302 kB)
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English version:
Sbornik: Mathematics, 2000, 191:2, 275–290

Bibliographic databases:

UDC: 517.518.23
MSC: 46E35
Received: 02.12.1997

Citation: L. K. Kusainova, “Embedding the weighted Sobolev space $W^l_p(\Omega;v)$ in the space $L_p(\Omega;\omega)$”, Mat. Sb., 191:2 (2000), 132–148; Sb. Math., 191:2 (2000), 275–290

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. L. K. Kussainova, “On oscillation of two terms linear differential equation with alternating potential”, Eurasian Math. J., 3:2 (2012), 135–140  mathnet  mathscinet  zmath
    2. L. K. Kusainova, A. Myrzagaliyeva, Ya. T. Sultanaev, “On the Boundedness of the Schrödinger Operator in Weighted Sobolev Spaces”, Math. Notes, 99:6 (2016), 948–953  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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