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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

Silvano Delladio*
Affiliation:
Dipartimento di Matematica, University of Trento, via Sommarive 14, Povo, I-38123Trento, Italy (silvano.delladio@unitn.it)

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.

Type
Research Article
Copyright
Copyright © The Author(s), 2020. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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