For annuli in the plane, the BV least gradient problem with BV boundary data is shown to be equivalent to a boundary-to-boundary optimal transport problem, and under admissibility conditions a unique solution with W^{1,p} regularity exists.
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Least gradient problem on annuli
For annuli in the plane, the BV least gradient problem with BV boundary data is shown to be equivalent to a boundary-to-boundary optimal transport problem, and under admissibility conditions a unique solution with W^{1,p} regularity exists.