A duality-based approach to gradient flows of linear growth functionals
Analysis of PDEs
2025-03-19 v2
Abstract
We study gradient flows of general functionals with linear growth with very weak assumptions. Classical results concerning characterisation of solutions require differentiability of the Lagrangian, as for the time-dependent minimal surface equation, or a special form of the Lagrangian as in the total variation flow. We propose to study this problem using duality techniques, give a general definition of solutions and prove their existence and uniqueness. This approach also allows us to reduce the regularity and structure assumptions on the Lagrangian.
Cite
@article{arxiv.2212.08725,
title = {A duality-based approach to gradient flows of linear growth functionals},
author = {Wojciech Górny and José M. Mazón},
journal= {arXiv preprint arXiv:2212.08725},
year = {2025}
}
Comments
31 pages. arXiv admin note: text overlap with arXiv:2105.11424