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On the comparison of the spaces $L^1BV(\mathbb{R}^n)$ and $BV(\mathbb{R}^n)$

Author: Yudi Soeharyadi
Journal: Proc. Amer. Math. Soc. 130 (2002), 405-412
MSC (2000): Primary 46B99, 35D10, 47H20, 47D03
Published electronically: May 25, 2001
MathSciNet review: 1862119
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The notion of $L^1$-variation and the space $L^1BV$ arise in the study of regularity properties of solutions to perturbed conservation laws. In this article we show that this notion is equivalent to variation in the regular sense, and therefore the space $L^1BV$ is the same as the space $BV$ in the sense of Cesari-Tonelli. We also point out some connection between the space $L^1BV$ and the Favard classes for translation semigroups.

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Additional Information

Yudi Soeharyadi
Affiliation: Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152
Address at time of publication: Department of Mathematics, Southern Illinois University, Carbondale, Illinois 62901-4408

Keywords: $L^1$-variation, variation, total variation, essential variation, conservation laws, perturbed conservation laws, $m$-dissipative operator, invariant set, Favard class
Received by editor(s): March 1, 2000
Received by editor(s) in revised form: June 12, 2000
Published electronically: May 25, 2001
Communicated by: Carmen C. Chicone
Article copyright: © Copyright 2001 American Mathematical Society