The Trace Theorem, the Luzin N- and Morse-Sard Properties for the Sharp Case of Sobolev-Lorentz Mappings.

Author: 

Korobkov, M
Kristensen, J

Publication Date: 

January 2018

Journal: 

Journal of geometric analysis

Last Updated: 

2019-10-18T17:40:51.693+01:00

Issue: 

3

Volume: 

28

DOI: 

10.1007/s12220-017-9936-7

page: 

2834-2856

abstract: 

We prove Luzin N- and Morse-Sard properties for mappings v:Rn→Rd of the Sobolev-Lorentz class Wp,1k , p=nk (this is the sharp case that guaranties the continuity of mappings). Our main tool is a new trace theorem for Riesz potentials of Lorentz functions for the limiting case q=p . Using these results, we find also some very natural approximation and differentiability properties for functions in Wp,1k with exceptional set of small Hausdorff content.

Symplectic id: 

735461

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article