Electron. J. Diff. Eqns., Vol. 2001(2001), No. 57, pp. 1-18.

On the ellipticity and solvability of an abstract second-order differential equation

Abdelillah El Haial & Rabah Labbas

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.

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Abdelillah El Haial
Universite du Havre, I.U.T,
B.P 4006, 76610 Le Havre, France
Rabah Labbas
Laboratoire de Mathematiques
Faculte des Scienceset Techniques
Universite du Havre
B.P 540, 76058 Le Havre Cedex, France
e-mail: Labbas@univ-lehavre.fr

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