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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 4(346), Pages 59–74 (Mi umn533)  

This article is cited in 104 scientific papers (total in 105 papers)

How to recognize constant functions. Connections with Sobolev spaces

H. Brezis

Université Pierre & Marie Curie, Paris VI

Abstract: A criterion for a function $f\in L^p$ to belong to $W^{1,p}$ $(p>1)$ or to $BV$ $(p=1)$ is given. Various integral conditions under which a measurable function is constant are discussed.

DOI: https://doi.org/10.4213/rm533

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English version:
Russian Mathematical Surveys, 2002, 57:4, 693–708

Bibliographic databases:

UDC: 517.98
MSC: 46E35
Received: 05.04.2002

Citation: H. Brezis, “How to recognize constant functions. Connections with Sobolev spaces”, Uspekhi Mat. Nauk, 57:4(346) (2002), 59–74; Russian Math. Surveys, 57:4 (2002), 693–708

Citation in format AMSBIB
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\pages 59--74
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\pages 693--708
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