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This article is cited in 23 scientific papers (total in 23 papers)
Embeddings and Separable Differential Operators in Spaces of Sobolev–Lions type
V. B. Shakhmurov Okan University
Abstract:
We study embedding theorems for anisotropic spaces of Bessel–Lions type $H_{p,\gamma}^l(\Omega;E_0,E)$, where $E_0$ and $E$ are Banach spaces. We obtain the most regular spaces $E_\alpha$ for which mixed differentiation operators $D^\alpha$ from $H_{p,\gamma}^l(\Omega;E_0,E)$ to $L_{p,\gamma}(\Omega;E_\alpha)$ are bounded. The spaces $E_\alpha$ are interpolation spaces between $E_0$ and $E$, depending on $\alpha=(\alpha_1,\alpha_2,\dots,\alpha_n)$ and $l=(l_1,l_2,\dots,l_n)$. The results obtained are applied to prove the separability of anisotropic differential operator equations with variable coefficients.
Received: 02.09.2005
Citation:
V. B. Shakhmurov, “Embeddings and Separable Differential Operators in Spaces of Sobolev–Lions type”, Mat. Zametki, 84:6 (2008), 907–926; Math. Notes, 84:6 (2008), 842–858
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https://www.mathnet.ru/eng/mzm6567https://doi.org/10.4213/mzm6567 https://www.mathnet.ru/eng/mzm/v84/i6/p907
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Abstract page: | 731 | Full-text PDF : | 212 | References: | 91 | First page: | 9 |
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