A NOTE ON POSITIVITY OF DIFFERENTIAL OPERATOR WITH SAMARSKII-IONKIN-TYPE CONDITION
Journal of Mathematical Sciences (United States), vol.301, no.1, pp.85-99, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 301 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1007/s10958-025-08068-6
- Journal Name: Journal of Mathematical Sciences (United States)
- Journal Indexes: Scopus, MathSciNet, zbMATH
- Page Numbers: pp.85-99
- Keywords: Banach Space, Interpolation Theorem, Positive Operator, Well-posedness of Parabolic Problems
- Hacettepe University Affiliated: Yes
Abstract
This article investigates a second-order differential operator with Samarskii-Ionkin-type conditions. It proves that the operator is positive in C[0, 1]. Moreover, it investigates the structure of the interpolation spaces generated by this operator. Furthermore, for each η∈(0,2-1), it proves the topological equivalence of this interpolation space and the Hölder space C∘2η[0,1]. Hence, it establishes that this operator is positive in C∘2η[0,1]. It also applies theoretical outcomes to obtain noval coercivity estimates for solutions of some specific type parabolic equation.