A NOTE ON POSITIVITY OF DIFFERENTIAL OPERATOR WITH SAMARSKII-IONKIN-TYPE CONDITION

Ashyralyev A., SÖZEN Y.

Journal of Mathematical Sciences (United States), 2026 (Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2026
  • Doi Numarası: 10.1007/s10958-025-08068-6
  • Dergi Adı: Journal of Mathematical Sciences (United States)
  • Derginin Tarandığı İndeksler: Scopus, MathSciNet, zbMATH
  • Anahtar Kelimeler: Banach Space, Interpolation Theorem, Positive Operator, Well-posedness of Parabolic Problems
  • Hacettepe Üniversitesi Adresli: Evet

Özet

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.