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Asymptotic Behavior of Solutions of Boundary-Value Problems for the Equation Δu − ku = f in a Layer

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Abstract

For the solutions of boundary-value problems for the equation Δu − ku = f in the layer

$$ \varPi =\left\{ {\left( {x^{\prime},{x_n}} \right)\in {{\mathbb{R}}^n}|{x}^{\prime}\in {{\mathbb{R}}^{n-1 }},{x_n}\in \left( {a,b} \right)} \right\},\quad -\infty <a<b<+\infty, \quad n\geq 3, $$

one obtains the first term of their asymptotics at infinity.

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References

  1. M. G. Gasymov and G. I. Aslanov, “On the existence and asymptotic behavior of weak solutions of the Neumann problem for second-order elliptic equations in unbounded domains of layer type,” Differ. Uravn., 37, No. 12, 1618–1628 (2001).

    MathSciNet  Google Scholar 

  2. V. A. Nikishkin, “Estimates of solutions of elliptic boundary-value problems in a layer,” Differ. Uravn., 47, No. 3, 450–454 (2011).

    MathSciNet  Google Scholar 

  3. V. A. Nikishkin, “Estimates of solutions of elliptic boundary-value problems for elliptic systems in a layer,” Funkts. Anal. Prilozh., 45, No. 2, 60–70 (2011).

    Article  MathSciNet  Google Scholar 

  4. S. Mizohata, Theory of Partial Differential Equations [Russian translation], Mir, Moscow (1977).

    Google Scholar 

  5. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  6. A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Nauka, Moscow (1983).

    Google Scholar 

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Authors and Affiliations

  1. Moscow State University of Economics, Statistics, and Informatics, Moscow, Russia

    V. A. Nikishkin

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  1. V. A. Nikishkin
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Correspondence to V. A. Nikishkin.

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To Prof. V. A. Kondratiev with gratitude

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 29, Part II, pp. 390–396, 2013.

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Nikishkin, V.A. Asymptotic Behavior of Solutions of Boundary-Value Problems for the Equation Δu − ku = f in a Layer. J Math Sci 197, 395–398 (2014). https://doi.org/10.1007/s10958-014-1720-7

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  • DOI: https://doi.org/10.1007/s10958-014-1720-7

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