Anzellotti's pairing theory and the Gauss--Green theorem

Abstract

In this paper we obtain a very general Gauss-Green formula for weakly differentiable functions and sets of finite perimeter. This result is obtained by revisiting Anzellotti's pairing theory and by characterizing the measure pairing $(\mathbf{A},Du)$ when $\mathbf{A}$ is a bounded divergence measure vector field and $u$ is a bounded function of bounded variation.

27 pages

References in corpus (5)

• An extension of the pairing theory between divergence-measure fields and BV functions
• Rigidity and trace properties of divergence-measure vector fields
• Nonlinear diffusion in transparent media: the resolvent equation
• Elliptic problems involving the 1--Laplacian and a singular lower order term
• Existence and comparison results for an elliptic equation involving the $1$-Laplacian and $L^1$-data

Cited by in corpus (8)

• The Dirichlet problem for singular elliptic equations with general nonlinearities
• The Dirichlet problem for the $1$-Laplacian with a general singular term and $L^1$-data
• An extension of the pairing theory between divergence-measure fields and BV functions
• Rigidity and trace properties of divergence-measure vector fields
• Finite energy solutions for nonlinear elliptic equations with competing gradient, singular and $L^1$ terms
• Fractional divergence-measure fields, Leibniz rule and Gauss-Green formula
• The Sattinger iteration method for 1-Laplace type problems and its application to concave-convex nonlinearities
• Geometric criteria for the existence of capillary surfaces in tubes