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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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
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author Korobkov, Mikhail V.
Kristensen, Jan
author_facet Korobkov, Mikhail V.
Kristensen, Jan
author_sort Korobkov, Mikhail V.
collection PubMed
description 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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spelling pubmed-62941812018-12-28 The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings Korobkov, Mikhail V. Kristensen, Jan J Geom Anal Article 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. Springer US 2017-10-14 2018 /pmc/articles/PMC6294181/ /pubmed/30839877 http://dx.doi.org/10.1007/s12220-017-9936-7 Text en © The Author(s) 2017 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Korobkov, Mikhail V.
Kristensen, Jan
The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title_full The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title_fullStr The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title_full_unstemmed The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title_short The Trace Theorem, the Luzin N- and Morse–Sard Properties for the Sharp Case of Sobolev–Lorentz Mappings
title_sort trace theorem, the luzin n- and morse–sard properties for the sharp case of sobolev–lorentz mappings
topic Article
url 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
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