On strong solvability of one boundary value problem for X-valued Laplace equation on half disc
Integral Transforms and Special Functions, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1080/10652469.2026.2694714
- Dergi Adı: Integral Transforms and Special Functions
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Academic Search Ultimate (EBSCO), Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: non-local BVP, strong solvability, t-basis, UMD space, X-valued Laplace equation
- Yıldız Teknik Üniversitesi Adresli: Evet
Özet
A boundary value problem is considered for an X-valued Laplace equation, where X is a Hilbert space. The considered problem has specific features: the solution is sought in an X-valued Sobolev space; the boundary conditions are nonlocal in nature; the boundary conditions of the corresponding spectral problem are regular, but not strongly regular in the sense of Birkhoff. To solve this problem, we use the concept of a t-basis generated by the tensor product (Formula presented.). The spectral problem possesses two series of asymptotically close eigenfunctions, which therefore do not form a basis in (Formula presented.). We construct a linear combination of eigenfunctions and establish the t-basisness of the resulting system for (Formula presented.). Using this fact, we prove the unique solvability of the BVP in Sobelev space (Formula presented.), where (Formula presented.). We also emphasize that the results obtained are new even in the scalar-valued case.