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

We prove Luzin N- and Morse–Sard properties for mappings [Formula: see text] of the Sobolev–Lorentz class [Formula: see text] , [Formula: see text] (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...

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Detalles Bibliográficos
Autores principales: Korobkov, Mikhail V., Kristensen, Jan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2017
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6294181/
https://www.ncbi.nlm.nih.gov/pubmed/30839877
http://dx.doi.org/10.1007/s12220-017-9936-7
Descripción
Sumario:We prove Luzin N- and Morse–Sard properties for mappings [Formula: see text] of the Sobolev–Lorentz class [Formula: see text] , [Formula: see text] (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 [Formula: see text] . Using these results, we find also some very natural approximation and differentiability properties for functions in [Formula: see text] with exceptional set of small Hausdorff content.

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