Electronic Journal of Differential Equations,
Vol. 2001(2001), No. 57, pp. 1-18.

Title: On the ellipticity and solvability of an abstract 
       second-order differential equation 
   
Authors:  Abdelillah El Haial (Univ. du Havre, France)
 Rabah Labbas (Univ. du Havre, France)

Abstract:  
 In this work we give some new results on a complete abstract 
 second-order differential equation of elliptic type in the
 non-homogeneous case.  Existence, uniqueness, and maximal regularity 
 of the strict solution are proved under some natural assumptions 
 which imply the ellipticity of the differential equation.
  
Submitted November 15, 1998. Published August 27, 2001.
Math Subject Classifications: 34G10, 35J25, 47D03.
Key Words: Abstract elliptic equations.