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

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Matematicheskie Zametki, 2008, Volume 84, Issue 6, Pages 907–926
DOI: https://doi.org/10.4213/mzm6567 (Mi mzm6567)

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

Full-text PDF (622 kB) Citations (23)

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DOI: https://doi.org/10.4213/mzm6567

Abstract: We study embedding theorems for anisotropic spaces of Bessel–Lions type

H_{p, γ}^{l} (Ω; E_{0}, E)

$H_{p,\gamma}^l(\Omega;E_0,E)$ , where

E_{0}

$E_0$ and

E

$E$ are Banach spaces. We obtain the most regular spaces

E_{α}

$E_\alpha$ for which mixed differentiation operators

D^{α}

$D^\alpha$ from

H_{p, γ}^{l} (Ω; E_{0}, E)

$H_{p,\gamma}^l(\Omega;E_0,E)$ to

L_{p, γ} (Ω; E_{α})

$L_{p,\gamma}(\Omega;E_\alpha)$ are bounded. The spaces

E_{α}

$E_\alpha$ are interpolation spaces between

E_{0}

$E_0$ and

E

$E$ , depending on

α = (α_{1}, α_{2}, \dots, α_{n})

$\alpha=(\alpha_1,\alpha_2,\dots,\alpha_n)$ and

l = (l_{1}, l_{2}, \dots, l_{n})

$l=(l_1,l_2,\dots,l_n)$ . The results obtained are applied to prove the separability of anisotropic differential operator equations with variable coefficients.

Received: 02.09.2005

English version:
Mathematical Notes, 2008, Volume 84, Issue 6, Pages 842–858
DOI: https://doi.org/10.1134/S0001434608110278

Bibliographic databases:

UDC: embedding operator, Hilbert space, Banach-valued function space, differential operator equation, operator-valued Fourier multiplier, interpolation of Banach spaces, probability space, UMD-space, Sobolev--Lions space

Language: Russian

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

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm6567

https://doi.org/10.4213/mzm6567

https://www.mathnet.ru/eng/mzm/v84/i6/p907

This publication is cited in the following 23 articles:

V. B. Shakhmurov, “Separability Properties of Differential Operators in Exterior Regions and Applications”, Lobachevskii J Math, 44:12 (2023), 5406
Veli Shakhmurov, Rishad Shahmurov, “The Regularity Properties and Blow-up of Solutions for Nonlocal Wave Equations and Applications”, Results Math, 77:6 (2022)
Shakhmurov V., “Fractional Abstract Differential Equations and Applications”, Bull. Malays. Math. Sci. Soc., 44:2 (2021), 1065–1078
Shakhmurov V.B., Shahmurov R., “The Improved Abstract Boussinesq Equations and Application”, Mediterr. J. Math., 18:6 (2021), 233
Musaev H.K., “The Cauchy Problem For Degenerate Parabolic Convolution Equation”, TWMS J. Pure Appl. Math., 12:2 (2021), 278–288
Agarwal R.P., Shakhmurov V.B., “Integral Type Cauchy Problem For Abstract Wave Equations and Applications”, Appl. Anal., 2021
Shakhmurov V.B., “The Cauchy Problem For Nonlocal Abstract Schrodinger Equations and Applications”, Anal. Math. Phys., 11:4 (2021), 147
Shakhmurov V., “Fractional Differential Operators in Vector-Valued Spaces and Applications”, Math. Inequal. Appl., 23:2 (2020), 521–538
Shakhmurov V., “Nonlocal Fractional Differential Equations and Applications”, Complex Anal. Oper. Theory, 14:4 (2020), 49
Shakhmurov V., “Regularity Properties of Nonlinear Abstract Schrodinger Equations and Applications”, Int. J. Math., 31:13 (2020), 2050105
Ragusa M.A., Shakhmurov V.B., “A Navier-Stokes-Type Problem With High-Order Elliptic Operator and Applications”, Mathematics, 8:12 (2020), 2256
Musaev H.K., “The Nonlocal Bvp For the System of Boussinesq Equation of Infinite Many Order”, Proceedings of the7Th International Conference on Control and Optimization With Industrial Applications, Vol. 1, eds. Fikret A., Tamer B., Baku State Univ, Inst Applied Mathematics, 2020, 290–292
Shakhmurov V., “Regularity Properties of Schrodinger Equations in Vector-Valued Spaces and Applications”, Forum Math., 31:1 (2019), 149–166
Shakhmurov V.B., Shahmurov R., “The Cauchy Problem For Boussinesq Equations With General Elliptic Part”, Anal. Math. Phys., 9:4 (2019), 1689–1709
Shakhmurov V.B., “Nonlocal problems for Boussinesq equations”, Nonlinear Anal.-Theory Methods Appl., 142 (2016), 134–151
Shakhmurov V., “Abstract Differential Equations with VMO Coefficients in Half Space and Applications”, Mediterr. J. Math., 13:4 (2016), 1765–1785
Shakhmurov V.B., “the Cauchy Problem For Generalized Abstract Boussinesq Equations”, Dyn. Syst. Appl., 25:1-2 (2016), 109–122
Shakhmurov V.B., Ekincioglu I., “Linear and Nonlinear Convolution Elliptic Equations”, Bound. Value Probl., 2013
Gusev N.A., “Asymptotic properties of linearized equations of low compressible fluid motion”, J. Math. Fluid Mech., 14:3 (2012), 591–618
Ragusa M.A., “Embeddings for Morrey-Lorentz spaces”, J. Optim. Theory Appl., 154:2 (2012), 491–499

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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