Rabah Labbas, Ahmed Medeghri, Boubaker-Khaled Sadallah
Abstract:
We give regularity results for solutions of a parabolic equation
in non-rectangular domains
with
.
The optimal regularity is obtained in the framework of the space
with
by considering the following cases:
(1) When
,
with a regular right-hand side belonging to a subspace
of
and under assumption
.
We use Labbas-Terreni results [11].
(2) When
with a right-hand side taken only
in
.
Our approach make use of the celebrated Dore-Venni
results [2].
Submitted July 16, 2004. Published March 29, 2005.
Math Subject Classifications: 35K05, 35K65, 35K90
Key Words: Sum of linear operators, diffusion equation,
non rectangular domain,bounded imaginary powers of operators
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Rabah Labbas Laboratoire de Mathématiques Université du Havre, U.F.R. Sciences et Techniques b.p. 540, 76058 Le Havre, France email: labbas@univ-lehavre.fr |
---|---|
Ahmed Medeghri Université de Mostaganem b.p. 188, 27000, Mostaganem, Algeria email: medeghri@univ-mosta.dz | |
Boubaker-Khaled Sadallah Ecole Normale Supérieure, Département de Maths, 16050 Kouba, Alger, Algeria email: sadallah@wissal.dz |
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