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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.

UDC: 517.98

MSC: 46E35

Received: 05.04.2002

DOI: 10.4213/rm533

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

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