The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space

John Urbas
November 2003
Calculus of Variations & Partial Differential Equations;Nov2003, Vol. 18 Issue 3, p307
Academic Journal
We prove a maximum principle for the curvature of spacelike admissible solutions of the equation of prescribed scalar curvature in Minkowski space. This enables us to extend to higher dimensions a recent existence result of Bayard for the Dirichlet problem in three and four dimensions. We also prove an interior curvature bound which permits us to prove the existence of locally smooth solutions in the case of spacelike affine boundary data. Uniform convexity of the boundary data is assumed throughout.


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