We prove that for a homogeneous linear partial differential operator A of order k <= 2 and an integrable map f taking values in the essential range of that operator, there exists a function u of special bounded variation satisfying Au(x) = f (x) almost everywhere.This extends a result of G. Alberti for gradients on R-N. In particular, for 0 <= m < N, it is shown that every integrable m-vector field is the absolutely continuous part of the boundary of a normal (m + 1)-current.
A Lebesgue-Lusin property for linear operators of first and second order
Arroyo-Rabasa Adolfo
2023-01-01
Abstract
We prove that for a homogeneous linear partial differential operator A of order k <= 2 and an integrable map f taking values in the essential range of that operator, there exists a function u of special bounded variation satisfying Au(x) = f (x) almost everywhere.This extends a result of G. Alberti for gradients on R-N. In particular, for 0 <= m < N, it is shown that every integrable m-vector field is the absolutely continuous part of the boundary of a normal (m + 1)-current.File in questo prodotto:
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