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The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. (English) Zbl 1080.53062
In this nice paper the author extend recent work by P. Bayard [Calc. Var. Partial Differ. Equ. 18, No. 1, 1–30 (2003; Zbl 1043.53027)] on the Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space. Among other results, the authors prove a maximum principle for the curvature of spacelike admissible solutions of the equation of prescribed scalar curvature in Minkowski space, and an interior curvature bound leading to the existence of locally smooth solutions in the case of spacelike affine boundary data.

MSC:
53C50 Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
35J60 Nonlinear elliptic equations
35J65 Nonlinear boundary value problems for linear elliptic equations
53C21 Methods of global Riemannian geometry, including PDE methods; curvature restrictions
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