Approximating the solutions of differential inclusions driven by measures
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The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded \(\varepsilon \)-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
KeywordsDifferential inclusions BV functions \(\varepsilon \)-Variations Regulated functions
Mathematics Subject ClassificationPrimary 26A45 Secondary 34A60 28B20 34A12 26A42
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