Labbas, RabahMedeghri, AhmedSadallah, Boubaker-Khaled2021-05-202021-05-202005-03-29Labbas, R., Medeghri, A., & Sadallah, B. K. (2005). An Lp-approach for the study of degenerate parabolic equations. <i>Electronic Journal of Differential Equations, 2005</i>(36), pp. 1-20.1072-6691https://hdl.handle.net/10877/13610We give regularity results for solutions of a parabolic equation in non-rectangular domains U = ∪t∈]0, 1[</sub> {t} x It with It = {x : 0 < x < φ(t)}. The optimal regularity is obtained in the framework of the space Lp with p > 3/2 by considering the following cases: (1) When φ(t) = tα, α > 1/2 with a p > 1 + α. We use Labbas-Terreni results [11]. (2) When φ(t) = t1/2 with a right-hand side taken only in Lp(U). Our approach make use of the celebrated Dore-Venni results [2].Text20 pages1 file (.pdf)enAttribution 4.0 InternationalSum of linear operatorsDiffusion equationNon rectangular domainBounded imaginary powers of operatorsArticle