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Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions
Mickaël Dos Santos1
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
Keywords: traces of functions of bounded variation, least gradient problem

Mickaël Dos Santos 1

1 Université Paris Est-Créteil, 61 avenue du Général de Gaulle, 94010 Créteil Cedex, France
Licence : CC-BY-NC-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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, Tome 9 (2017) no. 1, pp. 65-93. doi: 10.5802/cml.36

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

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

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

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