https://neckpinch.com/authors/alice-marveggio/New arXiv papers by Alice Marveggio, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2412.02567arxiv:2412.02567Tue, 03 Dec 2024 00:00:00 GMTLikhit Ganedi, Alice Marveggio, Kerrek Stinson — We consider a variational model for heterogeneous phase separation, based on a diffuse interface energy with moving wells. Our main result identifies the asymptotic behavior of the first variation of the phase field energies as the width of the diffuse interface vanishes. This convergence result allows us to deduce a Gibbs-Thomson relation for heterogeneous surface tensions. Proceeding from this information, we prove that (weak) solutions of the Allen-Cahn equation with space dependent potential converge to a BV solution of weighted mean curvature flow, under an energy convergence hypothesis. Additionally, relying on the relative energy technique, we establish a weak-strong uniqueness principle for solutions of weighted mean curvature flow.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2404.02884arxiv:2404.02884Wed, 03 Apr 2024 00:00:00 GMTJulian Fischer, Sebastian Hensel, Alice Marveggio, Maximilian Moser — We prove a weak-strong uniqueness principle for varifold-BV solutions to planar multiphase mean curvature flow beyond a circular topology change: Assuming that there exists a classical solution with an interface that becomes increasingly circular and shrinks to a point, any varifold-BV solution with the same initial interface must coincide with it, and any varifold-BV solution with similar initial data must undergo the same type of topology change. Our result illustrates the robustness of the relative energy method for establishing weak-strong uniqueness principles for interface evolution equations, showing that it may also be applied beyond certain topological changes.Mean curvature flowWeak & singular flowsStability & uniquenessPhase fields & multiphase flows https://arxiv.org/abs/2203.17143arxiv:2203.17143Thu, 31 Mar 2022 00:00:00 GMTJulian Fischer, Alice Marveggio — Phase-field models such as the Allen-Cahn equation may give rise to the formation and evolution of geometric shapes, a phenomenon that may be analyzed rigorously in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn equation with a potential with N≥ 3 distinct minima has been conjectured to describe the evolution of branched interfaces by multiphase mean curvature flow. In the present work, we give a rigorous proof for this statement in two and three ambient dimensions and for a suitable class of potentials: As long as a strong solution to multiphase mean curvature flow exists, solutions to the vectorial Allen-Cahn equation with well-prepared initial data converge towards multiphase mean curvature flow in the limit of vanishing interface width parameter ε↘ 0. We even establish the rate of convergence O(ε^(1/2)). Our approach is based on the gradient flow structure of the Allen-Cahn equation and its limiting motion: Building on the recent concept of "gradient flow calibrations" for multiphase mean curvature flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation with multi-well potential. This enables us to overcome the limitations of other approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn operator or additional convergence hypotheses for the energy at positive times.Mean curvature flowStability & uniquenessPhase fields & multiphase flows