Electronic Journal of Differential Equations,
Vol. 2005(2005), No. 36, pp. 1-20.
Title: An Lp-approach for the study of degenerate
parabolic equations
Authors: Rabah Labbas (Univ. du Havre, Le Havre, France, France)
Ahmed Medeghri (Univ. de Mostaganem, Algeria)
Boubaker-Khaled Sadallah (Ecole Normale Sup., Alger, Algeria)
Abstract:
We give regularity results for solutions of a parabolic equation
in non-rectangular domains
$U=\cup_{t\in ] 0,1[}\{ t\} \times I_{t}$ with
$I_{t}=\{x:03/2$ by considering the following cases:
(1) When $\varphi (t)=t^{\alpha }$, $\alpha >1/2$
with a regular right-hand side belonging to a subspace
of $L^{p}(U)$ and under assumption $p>1+\alpha $.
We use Labbas-Terreni results [11].
(2) When $\varphi (t)=t^{1/2}$ with a right-hand side taken only
in $L^{p}(U)$. 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