On Solvability Of One Boundary Value Problem For Laplace Equation in Banach-Hardy Classes
Journal of Contemporary Applied Mathematics, cilt.15, sa.1, ss.25-43, 2025 (Scopus)
- 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
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- 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.