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1. CJM 2000 (vol 52 pp. 757)

Hanani, Abdellah
 Le problÃ¨me de Neumann pour certaines Ã©quations du type de Monge-AmpÃ¨re sur une variÃ©tÃ© riemannienne Let $(M_n,g)$ be a strictly convex riemannian manifold with $C^{\infty}$ boundary. We prove the existence\break of classical solution for the nonlinear elliptic partial differential equation of Monge-Amp\`ere:\break $\det (-u\delta^i_j + \nabla^i_ju) = F(x,\nabla u;u)$ in $M$ with a Neumann condition on the boundary of the form $\frac{\partial u}{\partial \nu} = \varphi (x,u)$, where $F \in C^{\infty} (TM \times \bbR)$ is an everywhere strictly positive function satisfying some assumptions, $\nu$ stands for the unit normal vector field and $\varphi \in C^{\infty} (\partial M \times \bbR)$ is a non-decreasing function in $u$. Keywords:connexion de Levi-Civita, Ã©quations de Monge-AmpÃ¨re, problÃ¨me de Neumann, estimÃ©es a priori, mÃ©thode de continuitÃ©Categories:35J60, 53C55, 58G30
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