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Journal of Mathematical Sciences

, Volume 197, Issue 3, pp 395–398 | Cite as

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

  • V. A. Nikishkin
Article
  • 39 Downloads

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.

Keywords

Asymptotic Behavior Weak Solution Fundamental Solution Elliptic System Neumann Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 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).MathSciNetGoogle Scholar
  2. 2.
    V. A. Nikishkin, “Estimates of solutions of elliptic boundary-value problems in a layer,” Differ. Uravn., 47, No. 3, 450–454 (2011).MathSciNetGoogle Scholar
  3. 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).CrossRefMathSciNetGoogle Scholar
  4. 4.
    S. Mizohata, Theory of Partial Differential Equations [Russian translation], Mir, Moscow (1977).Google Scholar
  5. 5.
    V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1971).Google Scholar
  6. 6.
    A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Special Functions [in Russian], Nauka, Moscow (1983).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Moscow State University of Economics, Statistics, and InformaticsMoscowRussia

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