Lipschitz homotopy and density of Lipschitz mappings in Sobolev spaces
نویسندگان
چکیده
منابع مشابه
Lipschitz Spaces and Harmonic Mappings
In [11] the author proved that every quasiconformal harmonic mapping between two Jordan domains with C, 0 < α ≤ 1, boundary is biLipschitz, providing that the domain is convex. In this paper we avoid the restriction of convexity. More precisely we prove: any quasiconformal harmonic mapping between two Jordan domains Ωj , j = 1, 2, with C, j = 1, 2 boundary is bi-Lipschitz.
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Let X be a countable discrete metric space and let XX denote the family of all functions on X. In this article, we consider the problem of finding the least cardinality of a subset A of XX such that every element of XX is a finite composition of elements of A and Lipschitz functions on X. It follows from a classical theorem of Sierpiński that such an A either has size at most 2 or is uncountabl...
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ژورنال
عنوان ژورنال: Annales Academiae Scientiarum Fennicae Mathematica
سال: 2014
ISSN: 1239-629X,1798-2383
DOI: 10.5186/aasfm.2014.3932