Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 05, pp. 1-33.

Title: Fractional-power approach for  solving  complete
       elliptic abstract differential equations with variable-operator
       coefficients

Author: Fatiha Boutaous (Univ. Saad Dahlab, Blida, Algerie)
        Rabah Labbas (Univ. du Havre, Le Havre Cedex, France)
	Boubaker-Khaled Sadallah (Ecole Normale Superieure, Algerie)

Abstract:
 This work is devoted to the study of a complete abstract
 second-order differential equation of elliptic type with
 variable operators as coefficients.
 A similar equation was studied by  Favini et al [6] using  
 Green's kernels and Dunford functional calculus. Our approach 
 is based on the  semigroup theory, the fractional powers
 of linear operators, and the Dunford's functional calculus.
 We will prove the main result on the existence and uniqueness
 of a strict solutions using combining assumptions from
 Yagi [16], Da Prato-Grisvard [3], and Acquistapace-Terreni [1].

Submitted June 14, 2011. Published January 09, 2012.
Math Subject Classifications: 34G10, 34K10, 34K30,35J25, 44A45, 47D03.
Key Words: Fractional powers of linear operators; analytic semigroup; 
           strict solution; Dunford's functional calculus.