Résumé:
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 .
