Fredholmness of the Dirichlet Problem for 2mth-Order Elliptic Equations in Grand Sobolev Spaces

Bilalov B. T., Sadigova S. R., Nasibova N. P.

Mathematical Methods in the Applied Sciences, 2025 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1002/mma.11098
  • Dergi Adı: Mathematical Methods in the Applied Sciences
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: 2mth-order elliptic equation, Fredholmness, grand Sobolev spaces, strong solution
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

In this paper, on a bounded domain (Formula presented.) with a sufficiently smooth boundary (Formula presented.), it is considered a uniformly elliptic equation of (Formula presented.) th order, the coefficients of which are continuous in the principal part. Grand Lebesgue space (Formula presented.), is studied. This space is nonseparable, and it is defined a separable subspace (Formula presented.) of (Formula presented.), in which infinitely differentiable functions are dense. Furthermore, the grand Sobolev space (Formula presented.) of (Formula presented.) th-order differentiable in the Sobolev sense functions is introduced. This space is generated by the subspace (Formula presented.). For the given equation, a Schauder-type estimate up to the boundary is proved. Using this estimate, we establish an a priori estimate and then the Fredholmness of the (Formula presented.) th-order elliptic equation under consideration in (Formula presented.). By a solution, we mean a strong solution.