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On the Weak Solvability of a Nonlocal Boundary Value Problem for the Laplace Equation in an Unbounded Domain

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Abstract

A nonlocal problem for the Laplace equation in an unbounded domain is considered. A weak solution of this problem is determined in weighted Sobolev spaces generated by a weighted mixed norm. The correct solvability of this problem is proved by the Fourier method. In a weak formulation, this problem is apparently considered for the first time.

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ACKNOWLEDGMENTS

The author expresses deep gratitude to Professor B.T. Bilalov for the formulation of the problem and the attention paid to its solution.

Funding

This work is supported by the Science Development Foundation under the President of the Republic of Azerbaijan—Grant ‘‘Karabakh is Azerbaijan!’’

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Authors and Affiliations

  1. Azerbaijan State Oil and Industry University, Baku, Azerbaijan

    N. P. Nasibova

  2. Nakhchivan State University, Nakhchivan, Azerbaijan

    A. R. Safarova

Authors
  1. N. P. Nasibova
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  2. A. R. Safarova
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Corresponding authors

Correspondence to N. P. Nasibova or A. R. Safarova.

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(Submitted by T. K. Yuldashev)

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Nasibova, N.P., Safarova, A.R. On the Weak Solvability of a Nonlocal Boundary Value Problem for the Laplace Equation in an Unbounded Domain. Lobachevskii J Math 44, 2810–2821 (2023). https://doi.org/10.1134/S1995080223070302

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  • DOI: https://doi.org/10.1134/S1995080223070302

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