Minimizing Movements for Anisotropic and Inhomogeneous Mean Curvature Flows

Abstract: 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.