Journal of geometric analysis
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.
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