Abstract
We consider the anisotropic mean curvature flow of entire Lipschitz graphs. We prove existence and uniqueness of expanding self-similar solutions which are asymptotic to a prescribed cone, and we characterize the long time behavior of solutions, after suitable rescaling, when the initial datum is a sublinear perturbation of a cone. In the case of regular anisotropies, we prove the stability of self-similar solutions asymptotic to strictly mean convex cones, with respect to perturbations vanishing at infinity. We also show the stability of hyperplanes, with a proof which is novel also for the isotropic mean curvature flow.
Funder
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Ministero dell’Istruzione, dell’Università e della Ricerca
Subject
Computational Mathematics,Control and Optimization,Control and Systems Engineering
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Cited by
3 articles.
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