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The identity G(D)f = F for a linear partial differential operator G(D). Lusin type and structure results in the non-integrable case
Published online by Cambridge University Press: 26 November 2020
Abstract
We prove a Lusin type theorem for a certain class of linear partial differential operators G(D), reducing to [1, Theorem 1] when G(D) is the gradient. Moreover, we describe the structure of the set {G(D)f = F}, under assumptions of non-integrability on F, in terms of lower dimensional rectifiability and superdensity. Applications to Maxwell type system and to multivariable Cauchy–Riemann system are provided.
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- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 6 , December 2021 , pp. 1893 - 1919
- Copyright
- Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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