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
 $I_{t}=\{x:0<x<\varphi (t)\}$.
 The optimal regularity is obtained in the framework of the space
 $L^{p}$ with  $p>3/2$ 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