Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions

Characteristic functions on the boundary of a planar domain need not be traces of least gradient functions

Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc.

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Veröffentlicht in:arXiv.org 2017-03
1. Verfasser: Mickael Dos Santos
Format: Artikel
Sprache:eng
Schlagworte:
Characteristic functions
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Zusammenfassung:Given a smooth bounded planar domain, we construct a compact set on the boundary s.t. its characteristic function is not the trace of a least gradient function. This generalize the construction of Spradlin and Tamasan [ST14] on the disc.
ISSN:2331-8422