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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… Click to show full 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.
Keywords:
type;
linear partial;
partial differential;
lusin type
Journal Title: Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
Year Published: 2020
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Journal Title: Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!