Dirichlet problem for space-like hypersurfaces with prescribed scalar curvature in $\mathbb R^{n,1}$

Pierre Bayard
September 2003
Calculus of Variations & Partial Differential Equations;Sep2003, Vol. 18 Issue 1, p1
Academic Journal
We study the Dirichlet problem for the fully nonlinear elliptic partial differential equation of second order expressing the prescription of the m th symmetric function of the principal curvatures of a spacelike hypersurface in the Minkowski space $\mathbb R^{n,1}.$ We completely solve the prescribed lorentzian scalar curvature equation ( m=2) in ambiant dimension 4, if the datas are strictly convex.


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