On Some Elliptic Problems with Nonlocal Boundary Coefficient-operator Conditions in the Framework of Hölderian Spaces

Houari Hammou , Rabah Labbas (1) , Stéphane Maingot (1) , Ahmed Medeghri

1 LMAH - Laboratoire de Mathématiques Appliquées du Havre

In this paper we give some new results on second order differential-operator equations of elliptic type with nonregular boundary conditions with coefficient-operator. The study is developped in Hölder spaces and uses the reduction method of S. G. Krein. Necessary and sufficient conditions of compatibility are established to obtain different types of solutions. Maximal regularity properties are also studied.

Mots clés: ''Nonlocal boundary conditions''; ''fractional powers of operators''; '' interpolation spaces''; ''semigroup theory''; Nonlocal boundary conditions; fractional powers of operators; interpolation spaces; semigroup theory

Domaines: Equations aux dérivées partielles [math.AP]

Houari Hammou, Rabah Labbas, Stéphane Maingot, Ahmed Medeghri. On Some Elliptic Problems with Nonlocal Boundary Coefficient-operator Conditions in the Framework of Hölderian Spaces. Electronic Journal of Qualitative Theory of Differential Equations, 2013, N°. 36, pp.1-32. ⟨hal-00950065⟩