On the comparison of the spaces $L^1BV(\mathbb {R}^n)$ and $BV(\mathbb {R}^n)$
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Abstract:
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.References
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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
- Email: ysoehryd@memphis.edu, ysoeharyadi@math.siu.edu
- 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
- © Copyright 2001 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 130 (2002), 405-412
- MSC (2000): Primary 46B99, 35D10, 47H20, 47D03
- DOI: https://doi.org/10.1090/S0002-9939-01-06044-0
- MathSciNet review: 1862119