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This article is cited in 5 scientific papers (total in 5 papers)
Interpolation of Weighted Sobolev Spaces
S. G. Pyatkov Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
In the present article, we describe the spaces (Hmp,Ψ(Ω),Lp,ω(Ω))θ,p, where the norms on Hmp,Ψ(Ω) and on Lp,ω(Ω) are defined as follows:
‖u‖pHmp,Ψ(Ω)=∫Ω∑|α|⩽mωα|Dαu(x)|pdx,‖u‖pLp,ω(Ω)=∫Ωω(x)|u(x)|pdx,
with ωα, ω continuous positive functions on Ω. The results obtained are applicable to studying elliptic eigenvalue problems with an indefinite weight function.
Key words:
interpolation space, weighted Sobolev space, Besov space, Hardy inequality.
Received: 08.12.1998
Citation:
S. G. Pyatkov, “Interpolation of Weighted Sobolev Spaces”, Mat. Tr., 4:1 (2001), 122–173; Siberian Adv. Math., 10:3 (2000), 83–132
Linking options:
https://www.mathnet.ru/eng/mt8 https://www.mathnet.ru/eng/mt/v4/i1/p122
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