Mediterranean Journal of Mathematics

, Volume 10, Issue 1, pp 157–175 | Cite as

Laplace Equation on a Domain With a Cuspidal Point in Little Hölder Spaces

  • Belkacem Chaouchi
  • Rabah Labbas
  • Boubaker-Khaled Sadallah
Article

Abstract

In this paper, we give new results about existence, uniqueness and regularity properties for solutions of Laplace equation
$$\Delta u = h \quad {\rm in} \, \Omega$$
where Ω is a cusp domain. We impose nonhomogeneous Dirichlet conditions on some part of ∂Ω. The second member h will be taken in the little Hölder space \({h^{2 \sigma}(\bar{\Omega})}\) with \({\sigma \, \in \, ]0, \, 1/2[}\) . Our approach is based essentially on the study of an abstract elliptic differential equation set in an unbounded domain. We will use the continuous interpolation spaces and the generalized analytic semigroup theory.

Mathematics Subject Classification (2010)

Primary 12H20 Secondary 34G10 35J25 44A45 

Keywords

Abstract differential equation of elliptic type little Hölder space cuspidal point interpolation space 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  • Belkacem Chaouchi
    • 1
  • Rabah Labbas
    • 2
  • Boubaker-Khaled Sadallah
    • 3
  1. 1.Laboratoire de l’Energie et des Systèmes IntelligentsCentre Universitaire de Khemis MilianaKhemis MilianaAlgeria
  2. 2.Laboratoire de Mathématiques AppliquéesUniversité du Havre, U.F.R Sciences et TechniquesLe HavreFrance
  3. 3.Laboratoire PDE & Hist. MathsEcole Normale SupérieureKouba, AlgiersAlgeria

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