Étude de Problèmes aux Limites et de Transmission Régis par des Équations Di¤érentielles Abstraites de Type Elliptique à Coe¢ cients Opérateurs Variables dans les Espaces de Hölder

Abstract

We consider a family (P ) >0 of boundary value and transmission problems, which is repre- sented as an abstract second order di¤erential equation of elliptic type with variable operator coe¢ cients, in the framework of Hölder spaces, improving the work given by Belhamiti, O., Labbas, R., Lemrabet, K. and Medeghri, A (constant case) and also the study given by Favini, A., Labbas, R., Lemrabet, K. et Sadallah, B-K (variable case with di¤erentiability conditions on the resolvants). Here our essential hypothesis is inspired by these of Labbas, R. We use Dunford calculus, interpolation spaces, semigroups theory and some techniques develloped by Favini, A and Labbas, R in order to obtain existence, uniqueness and maximal regularity results for the strict solution of the problem for a xed .