Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows

Antonin Chambolle (1, 2) , Daniele de Gennaro (1) , Massimiliano Morini (3)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
3 Dipartimento di Matematica e Informatica [Parma]

In this paper we address anisotropic and inhomogeneous mean curvature flows with forcing and mobility, and show that the minimizing movements scheme converges to level set/viscosity solutions and to distributional solutions \textit{\`a la} Luckhaus-Sturzenhecker to such flows, the latter holding in low dimension and conditionally to a convergence of the energies. By doing so we generalize recent works concerning the evolution by mean curvature by removing the hypothesis of translation invariance, which in the classical theory allows to simplify many arguments.

Domaines: Mathématiques [math]

Antonin Chambolle, Daniele de Gennaro, Massimiliano Morini. Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows. Advances in Calculus of Variation, 2023, ⟨10.1515/acv-2022-0102⟩. ⟨hal-03894146v2⟩