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 ε-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
L. Di Piazza, V.M. (2019). Approximating the solutions of differential inclusions driven by measures. ANNALI DI MATEMATICA PURA ED APPLICATA, 198(6), 2123-2140 [10.1007/s10231-019-00857-6].
Approximating the solutions of differential inclusions driven by measures
L. Di Piazza;V. Marraffa
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2019-01-01
Abstract
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 ε-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
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