中文摘要：

文献提出的相对Sobolev空间的概念，它在研究二阶椭圆型偏微分方程解的问题上有重要的应用．把Sobolev空间中函数在欧氏空间有界区域的边界上取零值的等价条件推广到n-1维C^2流形上，并且对推广后的结论进行严格的证明，这一结论对于研究有不适定边界的二阶椭圆型偏微分方程的广义解有重要的理论价值．

英文摘要：

The notion of relative Sobolev Space is defined in Reference, and it is very important in discussing the elliptic partial differential equation of the second order with an ill-posed boundary. In this paper, the condition where the functions in Sobolve Space value zero is developed onto C^1 manifold of n-1 dimensions. The conclusion is proved strictly which is important in studying the generalized solution of ill-posed boundary problems.