6,516 research outputs found
Randomness and differentiability in higher dimensions
We present two theorems concerned with algorithmic randomness and
differentiability of functions of several variables. Firstly, we prove an
effective form of the Rademacher's Theorem: we show that computable randomness
implies differentiability of computable Lipschitz functions of several
variables. Secondly, we show that weak 2-randomness is equivalent to
differentiability of computable a.e. differentiable functions of several
variables.Comment: 19 page
Global smoothness of quasiconformal mappings in the Triebel-Lizorkin scale
We give sufficient conditions for quasiconformal mappings between simply
connected Lipschitz domains to have H\"older, Sobolev and Triebel-Lizorkin
regularity in terms of the regularity of the boundary of the domains and the
regularity of the Beltrami coefficients of the mappings. The results can be
understood as a counterpart for the Kellogg-Warchawski Theorem in the context
of quasiconformal mappings.Comment: 45 pages, 3 figure
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