On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces

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

Mathematical Methods in the Applied Sciences, 2024 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2024
  • Doi Numarası: 10.1002/mma.10279
  • 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: Dirichlet problem, polyharmonic equation, solvability, symmetric Sobolev spaces
  • Yıldız Teknik Üniversitesi Adresli: Evet

Özet

Let (Formula presented.) be a bounded domain with sufficiently smooth boundary (Formula presented.) and (Formula presented.) be a symmetric space defined on the measure space (Formula presented.). We consider a Dirichlet problem for (Formula presented.) -th order polyharmonic equation, and we establish its solvability (in strong sense) in Sobolev space (Formula presented.) generated by the norm of (Formula presented.). Such spaces include classical Sobolev spaces, Orlicz–Sobolev spaces, grand Sobolev spaces, and Marcinkiewicz–Sobolev spaces. The obtained results are new for these special cases, too.