An extension of the pairing theory between divergence-measure fields and BV functions

Abstract

In this paper we introduce a nonlinear version of the notion of Anzellotti's pairing between divergence--measure vector fields and functions of bounded variation, motivated by possible applications to evolutionary quasilinear problems. As a consequence of our analysis, we prove a generalized Gauss--Green formula.

arXiv comment23 pages. arXiv admin note: text overlap with arXiv:1708.00792

References in corpus (8)

• Anzellotti's pairing theory and the Gauss--Green theorem
• Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux
• The prescribed mean curvature equation in weakly regular domains
• Structure of solutions of multidimensional conservation laws with discontinuous flux and applications to uniqueness
• Rigidity and trace properties of divergence-measure vector fields
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Cited by in corpus (5)

• Anzellotti's pairing theory and the Gauss--Green theorem
• Cauchy Fluxes and Gauss-Green Formulas for Divergence-Measure Fields over General Open Sets
• Rigidity and trace properties of divergence-measure vector fields
• Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula
• Geometric criteria for the existence of capillary surfaces in tubes