The evoluted set at time T is the union of all images of an initial set A via the flow at times t ∈ (0, T). Its regularity is for interest for control, being the attainable set in several relevant examples.We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C1,1 domain.

When does the evoluted set have negligible boundary?

Rossi, Francesco
2021-01-01

Abstract

The evoluted set at time T is the union of all images of an initial set A via the flow at times t ∈ (0, T). Its regularity is for interest for control, being the attainable set in several relevant examples.We first show that it is not sufficient for A to have negligible boundary (i.e. zero Lebesgue measure) to ensure that the evoluted set has negligible boundary too. Instead, we prove that such property holds when A is a C1,1 domain.
2021
9781665436595
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11578/331152
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