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.
The identity G(D)f = F for a linear partial differential operator G(D). Lusin type and structure results in the non-integrable case / Delladio, Silvano. - In: PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH. SECTION A. MATHEMATICS. - ISSN 0308-2105. - 151:6(2021), pp. 1893-1919. [10.1017/prm.2020.85]
The identity G(D)f = F for a linear partial differential operator G(D). Lusin type and structure results in the non-integrable case
Delladio, Silvano
2021-01-01
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.| File | Dimensione | Formato | |
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