The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
The Dirichlet problem for the equation of prescribed scalar curvature in Minkowski space
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DOI：
10.1007/s00526-003-0206-0
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发表时间：
2003-11
影响因子：
2.1
通讯作者：
J. Urbas
中科院分区：
文献类型：
--
作者：
J. Urbas
证明了闵可夫斯基空间中规定标量曲率方程的类空间可容许解曲率的一个极大原理。这使我们能够将Bayard最近关于三维和四维狄利克雷问题的存在性结果推广到更高的维度。我们还证明了一个内曲率界，它允许我们证明在类空间仿射边界数据的情况下局部光滑解的存在性。自始至终假定边界数据具有一致的凸性。
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.