We prove a Cm Lusin approximation theorem for horizontal curves in the Heisenberg group. This states that every absolutely continuous horizontal curve whose horizontal velocity is m- 1 times L1 differentiable almost everywhere coincides with a Cm horizontal curve except on a set of small measure. Conversely, we show that the result no longer holds if L1 differentiability is replaced by approximate differentiability. This shows our result is optimal and highlights differences between the Heisenberg and Euclidean settings.

A Cm Lusin approximation theorem for horizontal curves in the Heisenberg group / Capolli, M.; Pinamonti, A.; Speight, G.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:1(2021), pp. 4901-4922. [10.1007/s00526-021-01923-9]

A Cm Lusin approximation theorem for horizontal curves in the Heisenberg group

Capolli M.;Pinamonti A.;
2021

Abstract

We prove a Cm Lusin approximation theorem for horizontal curves in the Heisenberg group. This states that every absolutely continuous horizontal curve whose horizontal velocity is m- 1 times L1 differentiable almost everywhere coincides with a Cm horizontal curve except on a set of small measure. Conversely, we show that the result no longer holds if L1 differentiability is replaced by approximate differentiability. This shows our result is optimal and highlights differences between the Heisenberg and Euclidean settings.
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Capolli, M.; Pinamonti, A.; Speight, G.
A Cm Lusin approximation theorem for horizontal curves in the Heisenberg group / Capolli, M.; Pinamonti, A.; Speight, G.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 60:1(2021), pp. 4901-4922. [10.1007/s00526-021-01923-9]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11572/341120
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