An Lp-approach for the Study of Degenerate Parabolic Equations

We give regularity results for solutions of a parabolic equation in non-rectangular domains U = ∪t∈]0,1[{t} × 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 regular right-hand side belonging to a subspace of Lp(U) and under assumption 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].