The Concept of a Trace and the Boundedness of the Trace Operator in Banach-Sobolev Function Spaces

Bilalov B., Sadigova S., Cetin Ş.

Numerical Functional Analysis and Optimization, vol.43, no.9, pp.1069-1094, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 9
  • Publication Date: 2022
  • Doi Number: 10.1080/01630563.2022.2085744
  • Journal Name: Numerical Functional Analysis and Optimization
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Communication Abstracts, Compendex, Computer & Applied Sciences, MathSciNet, Metadex, zbMATH, DIALNET, Civil Engineering Abstracts
  • Page Numbers: pp.1069-1094
  • Keywords: characterization, Sobolev Banach function space, trace operator, trace space
  • Istanbul Gelisim University Affiliated: No

Abstract

In this paper a Banach function space (b.f.s. in short) (Formula presented.) on a n-dimensional bounded domain Ω with Lebesgue measure is considered. The Banach function space (Formula presented.) on the (Formula presented.) -dimensional surface (Formula presented.) generated by the norm of the space (Formula presented.) is defined. The Sobolev function space (Formula presented.) is defined using the norm of the space (Formula presented.) as well as the concept of the trace of an arbitrary function from this space on the surface S. Based on this concept, the space of traces (Formula presented.) is defined and a characterization of this space is given. It was proved that it is boundedly embedded in the space (Formula presented.) Particular cases of a functional space (Formula presented.) can be Lebesgue spaces, Lebesgue spaces with variable summability exponents, Morrey space, Orlicz space, grand Lebesgue spaces and etc. The obtained results allow us to consider boundary value problems for differential equations in b.f.s. (Formula presented.).