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arXiv · 2212.08725

A duality-based approach to gradient flows of linear growth functionals

Wojciech Górny·José M. Mazón
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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.

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Wojciech Górny, José M. Mazón. 2022-12-16. A duality-based approach to gradient flows of linear growth functionals. https://arxiv.org/abs/2212.08725

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