CHARACTERISTIC FUNCTIONS ON THE BOUNDARY OF A PLANAR DOMAIN NEED NOT BE TRACES OF LEAST GRADIENT FUNCTIONS

Mickael dos Santos (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Equations aux dérivées partielles [math.AP]

Mickael dos Santos. CHARACTERISTIC FUNCTIONS ON THE BOUNDARY OF A PLANAR DOMAIN NEED NOT BE TRACES OF LEAST GRADIENT FUNCTIONS. 2015. ⟨hal-01216155v1⟩