标题： Lipschitz域的部分展开及其一些应用 显示英文标题

标题： Partial expansion of a Lipschitz domain and some applications

摘要： 我们证明了在一个Lipschitz域可以仅在其边界的一部分附近扩展，假设这部分由分段C1曲线围成。 扩展后的域以及扩展的部分仍然是Lipschitz的。 我们将此结果应用于证明标准向量Sobolev空间的一种正则分解，该空间在部分边界上的迹为零。 还指出了一种低正则性投影器到具有部分边界条件的有限元空间的应用。 显示英文摘要

摘要： We show that a Lipschitz domain can be expanded solely near a part of its boundary, assuming that the part is enclosed by a piecewise C1 curve. The expanded domain as well as the extended part are both Lipschitz. We apply this result to prove a regular decomposition of standard vector Sobolev spaces with vanishing traces only on part of the boundary. Another application in the construction of low-regularity projectors into finite element spaces with partial boundary conditions is also indicated.