Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms

Nathalie Grenon (1) , François Murat (2) , Alessio Porreta (3)

1 Centre Universitaire de Bourges
2 LJLL - Laboratoire Jacques-Louis Lions
3 Dipartimento di Matematica

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 - divA(x)Du + α0 u = 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.

Domaines: Analyse fonctionnelle [math.FA]

Nathalie Grenon, François Murat, Alessio Porreta. Existence and a priori estimate for elliptic problems with subquadratic gradient dependent terms. 2006. ⟨hal-00112178⟩