Revista Matemática Complutense

, Volume 24, Issue 1, pp 131–168 | Cite as

Study of boundary value and transmission problems governed by a class of variable operators verifying the Labbas-Terreni non commutativity assumption

  • Fatima Bouziani
  • Angelo Favini
  • Rabah Labbas
  • Ahmed Medeghri


The aim of this work is the study of some transmission problems, which are written as an abstract second order differential equation of elliptic type with variable operator coefficients, in the framework of Hölder spaces. Here, we do not assume the differentiability of the resolvent operators. However, we suppose that the family of variable operators verifies the Labbas-Terreni assumption inspired by the sum theory and similar to the Acquistapace-Terreni one. We use Dunford calculus, interpolation spaces and semigroup theory in order to obtain existence, uniqueness and maximal regularity results for the solution of the problem.


Abstract differential equation of elliptic type Transmission problems Maximal regularity Dunford operational calculus 

Mathematics Subject Classification (2000)

34G10 34K10 34K30 35J08 35J25 47D03 


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© Revista Matemática Complutense 2010

Authors and Affiliations

  • Fatima Bouziani
    • 1
  • Angelo Favini
    • 2
  • Rabah Labbas
    • 3
  • Ahmed Medeghri
    • 1
  1. 1.Laboratoire de Mathématiques Pures et AppliquéesUniversité de MostaganemMostaganemAlgeria
  2. 2.Dipartimento di MatematicaUniversità di Bologna, Piazza di Porta S. Donato, 5BolognaItaly
  3. 3.Laboratoire de Mathématiques AppliquéesUniversité du HavreLe HavreFrance

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