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.
Grenon, N., Murat, F., Porretta, A. (2006). 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]. COMPTES RENDUS MATHÉMATIQUE, 342(1), 23-28 [10.1016/j.crma.2005.09.027].
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]
PORRETTA, ALESSIO
2006-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
