no. 1
Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
Dos Santos, Mickaël1
1 Université Paris Est-Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
Confluentes Mathematici, Tome 9 (2017) no. 1, pp. 65-93.

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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DOI : 10.5802/cml.36
Classification : 26B30, 35J56
Mots clés : traces of functions of bounded variation, least gradient problem
Dos Santos, Mickaël 1

1 Université Paris Est-Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France 
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Dos Santos, Mickaël. Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions. Confluentes Mathematici, Tome 9 (2017) no. 1, pp. 65-93. doi : 10.5802/cml.36. http://www.numdam.org/articles/10.5802/cml.36/

[1] Anzellotti, G.; Giaquinta, M. Funzioni BV e tracce, Rend. Sem. Mat. Univ. Padova, Volume 60 (1978), pp. 1-21

[2] Giusti, E. Minimal surfaces and functions of bounded variation, Springer Science & Business Media, 1984 no. 80

[3] Spradlin, G.; Tamasan, A. Not All Traces on the Circle Come from Functions of Least Gradient in the Disk, Indiana Univ. Math. J., Volume 63 (2014) no. 3, pp. 1819-1837 | DOI

[4] Sternberg, P.; Williams, G.; Ziemer, W. Existence, uniqueness, and regularity for functions of least gradient., J. reine angew. Math., Volume 430 (1992), pp. 35-60

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