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Not all traces on the circle come from functions of least gradient in the disk

We provide an example of an $L^1$ function on the circle, which cannot be the trace of a function of bounded variation of least gradient in the disk. This shows that in theorems on existence and uniqueness of solutions to the least gradient problem, proven by Sternberg, Williams and Ziemer and published in 1992-1993, the hypothesis that the boundary data is continuous cannot be removed.

preprint2013arXivOpen access
Greg SpradlinAlexandru Tamasan
math.AP
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Open access2 authors1 topic
Imported metadata coverageMissing code, dataset, citation and institution fields are tracked without dominating the paper.Details
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Greg SpradlinAlexandru Tamasan

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