On the comparison of the spaces and

Author:
Yudi Soeharyadi

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

Published electronically:
May 25, 2001

MathSciNet review:
1862119

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

The notion of -variation and the space 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 is the same as the space in the sense of Cesari-Tonelli. We also point out some connection between the space 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

Email:
ysoehryd@memphis.edu, ysoeharyadi@math.siu.edu

DOI:
https://doi.org/10.1090/S0002-9939-01-06044-0

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