On Solvability Of One Boundary Value Problem For Laplace Equation in Banach-Hardy Classes

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Mamedov E., SEZER Y., Safarova A.

Journal of Contemporary Applied Mathematics, cilt.15, sa.1, ss.25-43, 2025 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 15 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.62476/jcam.151.3
  • Dergi Adı: Journal of Contemporary Applied Mathematics
  • Derginin Tarandığı İndeksler: Scopus
  • Sayfa Sayıları: ss.25-43
  • Anahtar Kelimeler: additive-invariant, Banach function space, Hardy class, Laplace equation, Noetherness, oblique derivatives
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

In this paper we consider the Dirichlet problem for the Laplace equation in Hardy classes generated by an additive-invariant Banach function space on the unit circle. It is shown that the classical Dirichlet problem for the Laplace equation has a unique solution for every boundary function from the considered space. It is considered a boundary problem for the Laplace equation with oblique derivatives in the Hardy classes generated by separable subspaces of rearrangement-invariant spaces in which the infinitely differentiable functions are dense. Noetherness of this problem is established and the index of this problem is calculated.