Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms [Existence et estimation a priori pour des problèmes elliptiques avec des termes sous quadratiques par rapport au gradient]

In this Note we prove an a priori estimate and the existence of a solution for a class of nonlinear elliptic problems whose model is - div A(x)Du + α0u = γ Du q + f(x), when 1 < q < 2 and f ∈ Lm(Ω) for some suitable m. The main interest of the result lies in the a priori estimate, the complete proof of which is given in the Note. © 2005 Académie des sciences. Published by Elsevier SAS. All rights reserved