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

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GASYMOV T., AKHMADLI B., ILDIZ Ü.

Turkish Journal of Mathematics, cilt.48, sa.1, ss.21-33, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 48 Sayı: 1
  • Basım Tarihi: 2024
  • Doi Numarası: 10.55730/1300-0098.3489
  • Dergi Adı: Turkish Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.21-33
  • Anahtar Kelimeler: Laplace equation, nonlocal problem, strong solution, weighted Sobolev space
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

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].