On solvability of polyharmonic Dirichlet problem in symmetric Sobolev spaces
Mathematical Methods in the Applied Sciences, vol.47, no.18, pp.14386-14401, 2024 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 47 Issue: 18
- Publication Date: 2024
- Doi Number: 10.1002/mma.10279
- Journal Name: Mathematical Methods in the Applied Sciences
- Journal Indexes: 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
- Page Numbers: pp.14386-14401
- Keywords: Dirichlet problem, polyharmonic equation, solvability, symmetric Sobolev spaces
- Yıldız Technical University Affiliated: Yes
Abstract
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.