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Published online by Cambridge University Press: 06 November 2023
We prove that for a homogeneous linear partial differential operator $\mathcal {A}$ of order $k \le 2$
and an integrable map $f$
taking values in the essential range of that operator, there exists a function $u$
of special bounded variation satisfying
. In particular, for $0 \le m < N$
, it is shown that every integrable $m$
-vector field is the absolutely continuous part of the boundary of a normal $(m+1)$
-current.