CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCJM
Abstract view

Le problème de Neumann pour certaines équations du type de Monge-Ampère sur une variété riemannienne

  Published:2000-08-01
 Printed: Aug 2000
  • Abdellah Hanani
Features coming soon:
Citations   (via CrossRef) Tools: Search Google Scholar:
Format:   HTML   LaTeX   MathJax   PDF   PostScript  

Abstract

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, équations de Monge-Ampère, problème de Neumann, estimées a priori, méthode de continuité connexion de Levi-Civita, équations de Monge-Ampère, problème de Neumann, estimées a priori, méthode de continuité
MSC Classifications: 35J60, 53C55, 58G30 show english descriptions Nonlinear elliptic equations
Hermitian and Kahlerian manifolds [See also 32Cxx]
unknown classification 58G30
35J60 - Nonlinear elliptic equations
53C55 - Hermitian and Kahlerian manifolds [See also 32Cxx]
58G30 - unknown classification 58G30
 

© Canadian Mathematical Society, 2014 : http://www.cms.math.ca/