Calculus of Variations and Geometric Measure Theory
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Seminari di Analisi Matematica tra Firenze, Pisa e Siena

Anisotropic mean curvature flow

Matteo Novaga (Dip. Mat. Univ. Pisa)

created by paolini on 30 Apr 2019

17 may 2019 -- 11:10   [open in google calendar]


I will present existence and uniqueness results for the anisotropic mean curvature flow with arbitrary mobility. This is achieved by introducing a new notion of solution to the corresponding level set formulation. Such a solution satisfies the comparison principle and a stability property with respect to the approximation by suitably regularized problems. The results are valid in any dimension and for arbitrary, possibly unbounded, initial closed sets. The approach accounts for the possible presence of a time-dependent bounded forcing term, with spatial Lipschitz continuity. As a byproduct of the analysis, the problem of the convergence of the Almgren-Taylor-Wang minimizing movements scheme to a unique “flat flow” in the case of general, possibly crystalline, anisotropies is settled

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