Variational Nonlinear and Nonlocal Curvature Flows
Analysis of PDEs
2025-06-09 v1
Abstract
We prove that the minimizing movements scheme \'a la Almgren-Taylor-Wang converges towards level-set solutions to a nonlinear version of nonlocal curvature flows with time-depending forcing term, in the rather general framework of variational curvatures introduced in \cite{ChaMorPon15}. The nonlinearity involved is assumed to satisfy minimal assumptions, namely continuity, monotonicity, and vanishing at zero. Under additional assumptions only on the curvatures involved, we establish uniqueness for level-set solutions.
Cite
@article{arxiv.2506.05951,
title = {Variational Nonlinear and Nonlocal Curvature Flows},
author = {Daniele De Gennaro},
journal= {arXiv preprint arXiv:2506.05951},
year = {2025}
}