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On the Morse–Sard property and level sets of Sobolev and BV functions Научная публикация

Журнал

Revista Matematica Iberoamericana
ISSN: 0213-2230

Вых. Данные

Год: 2013, Том: 29, Номер: 1, Страницы: 1-23 Страниц : 23 DOI: 10.4171/rmi/710

Ключевые слова

BV2 and W2,1 functions; Level sets; Luzin N property; Morse-Sard property

Авторы

Bourgain Jean ¹ , Korobkov Mikhail ^2,3 , Kristensen Jan ⁴

Организации

1	Institute for Advanced Study, Einstein Drive
2	Sobolev Institute of Mathematics
3	Novosibirsk State University
4	University of Oxford

We establish Luzin N and Morse–Sard properties for BV2 functions defined on open domains in the plane. Using these results we prove that almost all level sets are finite disjoint unions of Lipschitz arcs whose tangent vectors are of bounded variation. In the case of W2,1 functions we strengthen the conclusion and show that almost all level sets are finite disjoint unions of C1 arcs whose tangent vectors are absolutely continuous along these arcs.

Bourgain J. , Korobkov M. , Kristensen J.
On the Morse–Sard property and level sets of Sobolev and BV functions
Revista Matematica Iberoamericana. 2013. V.29. N1. P.1-23. DOI: 10.4171/rmi/710 WOS Scopus OpenAlex

Web of science:	WOS:000317157600001
Scopus:	2-s2.0-84876789647
OpenAlex:	W2963645786

БД	Цитирований
Scopus	38
OpenAlex	61
Web of science	36