Let $Omegasubset mathbb R^n$ be an open set. We show that for a continuous mapping $fin W^{1,n-1}(Omega, mathbb R^n)$ with $J_fin L^1(Omega)$ the validity of the Lusin (N) condition implies that the distributional Jacobian equals to the pointwise Jacobian.
Note on Lusin (N) condition and the distributional determinant / D'Onofrio, Luigi; Hencl, Stanislav; Malý, Jan; Schiattarella, Roberta. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 439:1(2016), pp. 171-182. [10.1016/j.jmaa.2016.01.002]
Note on Lusin (N) condition and the distributional determinant.
SCHIATTARELLA, ROBERTA
2016
Abstract
Let $Omegasubset mathbb R^n$ be an open set. We show that for a continuous mapping $fin W^{1,n-1}(Omega, mathbb R^n)$ with $J_fin L^1(Omega)$ the validity of the Lusin (N) condition implies that the distributional Jacobian equals to the pointwise Jacobian.File in questo prodotto:
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