On the transport of currents

DOI10.1007/S00032-024-00394-9MaRDI QIDQ6655898

Paolo Bonicatto

Publication date: 27 December 2024

Published in: Milan Journal of Mathematics (Search for Journal in Brave)

zbMATH Keywords

currentstransport equationcontinuity equationLie derivativedecomposability bundle

Mathematics Subject Classification ID

Transportation, logistics and supply chain management (90B06) Geometric measure and integration theory, integral and normal currents in optimization (49Q15) Transport equations (35Q49)

Cites Work

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• On the differentiability of Lipschitz functions with respect to measures in the Euclidean space
• Uniqueness of signed measures solving the continuity equation for Osgood vector fields
• Harmonic maps with defects
• The Jacobian and the Ginzburg-Landau energy
• Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
• Non-uniqueness of signed measure-valued solutions to the continuity equation in presence of a unique flow
• A uniqueness result for the continuity equation in two dimensions
• Space-time integral currents of bounded variation
• Variational convergence for functionals of Ginzburg-Landau type
• Currents in metric spaces
• Existence and uniqueness for the transport of currents by Lipschitz vector fields

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