No abstract

No abstract

We prove existence, regularity and nonexistence results for problems whose model is -Lambda u = f(x)/u gamma in Omega, with zero Dirichlet conditions on the boundary of an open, bounded subset Omega of R(N). Here gamma > 0 and f is a nonnegative function on Omega. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of gamma (which can be equal, larger or smaller than 1)

L'accès aux archives de la revue « Annales de l'I. H. P., section C » (http://www.elsevier.com/locate/anihpc) implique l'accord avec les conditions générales d'utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/

In this paper we give summability results for the gradients of solutions of nonlinear parabolic equations whose model iswith homogeneous Cauchy Dirichlet boundary conditions, where p>1 and + is a bounded measure on 0_(0, T ). We also study how the summability of the gradient improves if the measure + is a function in L m (0_(0, T )), with m``small.'' Moreover we give a new proof of the existence of a solution for problem (P). Academic Press