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Well-Posedness of the Generalized Samarskii–Ionkin Problem for Elliptic Equations in a Cylindrical Domain

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Abstract

We study the well-posedness of some analogs of the nonlocal Samarskii–Ionkin problem for second-order elliptic equations in Sobolev spaces. For the problems in question, existence and uniqueness theorems are proved for regular solutions, i.e., solutions that have all generalized Sobolev derivatives occurring in the corresponding equation. Some spectral problems for elliptic equations with the nonlocal Samarskii–Ionkin condition are studied.

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Funding

The work was carried out within the framework of the state order “Program of Fundamental Research of the Samara State University in the Field of Chemical Sciences and Materials Science,” subject no. FSSE-2020-0005.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia

    A. I. Kozhanov

  2. Samara State Technical University, Samara, 443100, Russia

    A. I. Kozhanov & A. V. Dyuzheva

Authors
  1. A. I. Kozhanov
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  2. A. V. Dyuzheva
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Correspondence to A. I. Kozhanov or A. V. Dyuzheva.

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Translated by V. Potapchouck

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Kozhanov, A.I., Dyuzheva, A.V. Well-Posedness of the Generalized Samarskii–Ionkin Problem for Elliptic Equations in a Cylindrical Domain. Diff Equat 59, 230–242 (2023). https://doi.org/10.1134/S0012266123020076

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