The Morse–Sard Theorem and Luzin N-Property › Обзор исследований

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The Morse–Sard Theorem and Luzin N-Property : A New Synthesis for Smooth and Sobolev Mappings. / Ferone, A.; Korobkov, M. V.; Roviello, A.

в: Siberian Mathematical Journal, Том 60, № 5, 01.09.2019, стр. 916-926.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

Harvard

Ferone, A, Korobkov, MV & Roviello, A 2019, 'The Morse–Sard Theorem and Luzin N-Property: A New Synthesis for Smooth and Sobolev Mappings', Siberian Mathematical Journal, Том. 60, № 5, стр. 916-926. https://doi.org/10.1134/S0037446619050148

APA

Ferone, A., Korobkov, M. V., & Roviello, A. (2019). The Morse–Sard Theorem and Luzin N-Property: A New Synthesis for Smooth and Sobolev Mappings. Siberian Mathematical Journal, 60(5), 916-926. https://doi.org/10.1134/S0037446619050148

Vancouver

Ferone A, Korobkov MV, Roviello A. The Morse–Sard Theorem and Luzin N-Property: A New Synthesis for Smooth and Sobolev Mappings. Siberian Mathematical Journal. 2019 сент. 1;60(5):916-926. doi: 10.1134/S0037446619050148

Author

Ferone, A. ; Korobkov, M. V. ; Roviello, A. / The Morse–Sard Theorem and Luzin N-Property : A New Synthesis for Smooth and Sobolev Mappings. в: Siberian Mathematical Journal. 2019 ; Том 60, № 5. стр. 916-926.

BibTeX

@article{e3c801a650654b4885598e477ea46c75,

title = "The Morse–Sard Theorem and Luzin N-Property: A New Synthesis for Smooth and Sobolev Mappings",

abstract = "Considering regular mappings of Euclidean spaces, we study the distortion of the Hausdorff dimension of a given set under restrictions on the rank of the gradient on the set. This problem was solved for the classical cases of k-smooth and H{\"o}lder mappings by Dubovitskii, Bates, and Moreira. We solve the problem for Sobolev and fractional Sobolev classes as well. Here we study the Sobolev case under minimal integrability assumptions that guarantee in general only the continuity of a mapping (rather than differentiability everywhere). Some new facts are found out in the classical smooth case. The proofs are mostly based on our previous joint papers with Bourgain and Kristensen (2013, 2015).",

keywords = "Bessel potential spaces, Hausdorff measure, H{\"o}lder mappings, Luzin N-property, Morse—Sard theorem, Sobolev-Lorentz mappings, Holder mappings, Morse-Sard theorem",

author = "A. Ferone and Korobkov, {M. V.} and A. Roviello",

year = "2019",

month = sep,

day = "1",

doi = "10.1134/S0037446619050148",

language = "English",

volume = "60",

pages = "916--926",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "5",

}

RIS

TY - JOUR

T1 - The Morse–Sard Theorem and Luzin N-Property

T2 - A New Synthesis for Smooth and Sobolev Mappings

AU - Ferone, A.

AU - Korobkov, M. V.

AU - Roviello, A.

PY - 2019/9/1

Y1 - 2019/9/1

N2 - Considering regular mappings of Euclidean spaces, we study the distortion of the Hausdorff dimension of a given set under restrictions on the rank of the gradient on the set. This problem was solved for the classical cases of k-smooth and Hölder mappings by Dubovitskii, Bates, and Moreira. We solve the problem for Sobolev and fractional Sobolev classes as well. Here we study the Sobolev case under minimal integrability assumptions that guarantee in general only the continuity of a mapping (rather than differentiability everywhere). Some new facts are found out in the classical smooth case. The proofs are mostly based on our previous joint papers with Bourgain and Kristensen (2013, 2015).

AB - Considering regular mappings of Euclidean spaces, we study the distortion of the Hausdorff dimension of a given set under restrictions on the rank of the gradient on the set. This problem was solved for the classical cases of k-smooth and Hölder mappings by Dubovitskii, Bates, and Moreira. We solve the problem for Sobolev and fractional Sobolev classes as well. Here we study the Sobolev case under minimal integrability assumptions that guarantee in general only the continuity of a mapping (rather than differentiability everywhere). Some new facts are found out in the classical smooth case. The proofs are mostly based on our previous joint papers with Bourgain and Kristensen (2013, 2015).

KW - Bessel potential spaces

KW - Hausdorff measure

KW - Hölder mappings

KW - Luzin N-property

KW - Morse—Sard theorem

KW - Sobolev-Lorentz mappings

KW - Holder mappings

KW - Morse-Sard theorem

UR - http://www.scopus.com/inward/record.url?scp=85073217967&partnerID=8YFLogxK

U2 - 10.1134/S0037446619050148

DO - 10.1134/S0037446619050148

M3 - Article

AN - SCOPUS:85073217967

VL - 60

SP - 916

EP - 926

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 5

ER -

ID: 21857998