On strong solvability of one nonlocal boundary value problem for Laplace equation in rectangle


Creative Commons License

GASYMOV T., AKHMADLI B., ILDIZ Ü.

Turkish Journal of Mathematics, vol.48, no.1, pp.21-33, 2024 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 48 Issue: 1
  • Publication Date: 2024
  • Doi Number: 10.55730/1300-0098.3489
  • Journal Name: Turkish Journal of Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.21-33
  • Keywords: Laplace equation, nonlocal problem, strong solution, weighted Sobolev space
  • Yıldız Technical University Affiliated: Yes

Abstract

One nonlocal boundary value problem for the Laplace equation in a bounded domain is considered in this work. The concept of a strong solution to this problem is introduced. The correct solvability of this problem in the Sobolev spaces generated by the weighted mixed norm is proved by the Fourier method. In a classic statement, this problem has been earlier considered by E.I.Moiseev [34]. A similar problem has been treated by M.E.Lerner and O.A.Repin [30].