Calculus of Variations and Geometric Measure Theory

C. Scheven - T. Schmidt

An Anzellotti type pairing for divergence-measure fields and a notion of weakly super-$1$-harmonic functions

created by schmidt on 20 Oct 2015
modified on 15 Mar 2023



Inserted: 20 oct 2015
Last Updated: 15 mar 2023

Year: 2015

ArXiv: 1701.02656 PDF

Annoucement of [2830] and [3320]


We study generalized products of divergence-measure fields and gradient measures of ${\rm BV}$ functions. These products depend on the choice of a representative of the ${\rm BV}$ function, and here we single out a specific choice which is suitable in order to define and investigate a notion of weak supersolutions for the $1$-Laplace operator.