On the equivalence of fractional-order Sobolev semi-norms
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2012
- DOI:
- 10.48550/arXiv.1211.0340
- arXiv:
- arXiv:1211.0340
- Bibcode:
- 2012arXiv1211.0340H
- Keywords:
-
- Mathematics - Functional Analysis;
- Mathematics - Numerical Analysis;
- 46E35;
- 47A30;
- 65N38
- E-Print:
- 16 pages, new version extended to include affine mappings, to appear in the Journal of Mathematical Analysis and Applications