科研之友
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摘要
We prove that, given a planar bi-Lipschitz map u defined on the boundary of the unit square, it is possible to extend it to a function v of the whole square, in such a way that v is still bi-Lipschitz. In particular, denoting by L and (L) over tilde the bi-Lipschitz constants of u and v, with our construction one has (L) over tilde <= CL4 (C being an explicit geometric constant). The same result was proved in 1980 by Tukia (see [3]), using a completely different argument, but without any estimate on the constant (L) over tilde. In particular, the function nu can be taken either smooth or (countably) piecewise affine.
- 出版日期2015-7
