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Mickaël Dos Santos
Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
Confluentes Mathematici, 9 no. 1 (2017), p. 65-93, doi: 10.5802/cml.36
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Class. Math.: 26B30, 35J56
Keywords: traces of functions of bounded variation, least gradient problem

Résumé - Abstract

Given a smooth bounded planar domain $Ø$, we construct a compact set on the boundary such that its characteristic function is not the trace of a least gradient function. This generalizes the construction of Spradlin and Tamasan [3] when $Ø$ is a disc.


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[2] E. Giusti, Minimal surfaces and functions of bounded variation, Springer Science & Business Media, 1984
[3] G. Spradlin & A. Tamasan, “Not All Traces on the Circle Come from Functions of Least Gradient in the Disk”, Indiana Univ. Math. J. 63 (2014) no. 3, p. 1819-1837 Article
[4] P. Sternberg, G. Williams & W. Ziemer, “Existence, uniqueness, and regularity for functions of least gradient.”, J. reine angew. Math. 430 (1992), p. 35-60
eISSN : 1793-7434