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

Christoph Scheven; Thomas Schmidt

arxiv: 1701.02656 · v1 · pith:THOA7SQTnew · submitted 2017-01-10 · 🧮 math.AP

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

Christoph Scheven , Thomas Schmidt This is my paper

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keywords choicedivergence-measurefieldsfunctionsnotionproductsanzellottidefine

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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.

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