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On the comparison of the spaces |
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| Authors: | Yudi Soeharyadi |
| Institution: | Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152 |
| Abstract: | The notion of |
| Keywords: | $L^1$-variation variation total variation essential variation conservation laws perturbed conservation laws $m$-dissipative operator invariant set Favard class |
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-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.