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arXiv · 1211.0340

On the equivalence of fractional-order Sobolev semi-norms

Norbert Heuer
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Abstract

We present various results on the equivalence and mapping properties under affine transformations of fractional-order Sobolev norms and semi-norms of orders between zero and one. Main results are mutual estimates of the three semi-norms of Sobolev-Slobodeckij, interpolation and quotient space types. In particular, we show that the former two are uniformly equivalent under affine mappings that ensure shape regularity of the domains under consideration.

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Norbert Heuer. 2012-11-02. On the equivalence of fractional-order Sobolev semi-norms. https://arxiv.org/abs/1211.0340

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