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On Some Multidimensional Limit Boundary Value Problems

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Abstract

We study solvability for a model elliptic pseudo-differential equation with an additional integral condition in Sobolev–Slobodetskii spaces in certain conical domains in Euclidean space. . Using the wave factorization for an elliptic symbol we construct a solution for this boundary value problem and study the behavior of the solution when parameters of cones tend to their extremal values. It was shown that for such a solvability we need certain additional condition besides presented integral condition.

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Authors and Affiliations

  1. Chair of Applied Mathematics and Computer Modeling, Belgorod State National Research University, 308015, Belgorod, Russia

    V. B. Vasilyev & Sh. H. Kutaiba

Authors
  1. V. B. Vasilyev
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  2. Sh. H. Kutaiba
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Correspondence to V. B. Vasilyev or Sh. H. Kutaiba.

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(Submitted by A. B. Muravnik)

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Vasilyev, V.B., Kutaiba, S.H. On Some Multidimensional Limit Boundary Value Problems. Lobachevskii J Math 42, 1219–1227 (2021). https://doi.org/10.1134/S1995080221060317

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  • DOI: https://doi.org/10.1134/S1995080221060317

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