Réarrangement relatif dans les équations elliptiques quasi-linéaires avec un second membre distribution: Application à un théorème d'existence et de régularité

AbstractIn this paper we are concerned with quasilinear elliptic equations, that is (P) Au + F(u,▽u) = T in Ω ⊂ R, u ϵ W01,p(Ω) ∩ L∞(Ω); where A is an operator of Leray-Lions type which is defined on W01p(Ω) ∩ L∞(Ω) (1 <p < +∞), F is a non-linear map having a suitable growth, and T is a distribution of W−1,r(Ω), r >N(p − 1)and r +̆p(p − 1). Using the techniques of the relative rearrangement (Ann. Scuola Norm. Sup. Pisa Cl Sci (4), in press), we give a precise a priori estimate of the solution u of (P) in L∞-norm. These estimates allow us to prove an existence theorem for (P) and to get the Hölder continuity of the solution