https://neckpinch.com/authors/rosivaldo-goncalves/New arXiv papers by Rosivaldo Gonçalves, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2606.29058/arxiv:2606.29058Sat, 27 Jun 2026 00:00:00 GMTEzequiel Barbosa, Rosivaldo Gonçalves, Luan de Figueiredo — We study a parabolic obstacle problem for surfaces evolving by anisotropic mean curvature flow subject to an obstacle constraint. Given a convex obstacle and initial data, we seek an evolving surface minimizing an anisotropic energy functional while remaining above the obstacle; as a special case, this framework includes the anisotropic Stefan problem, where the free boundary represents a phase transition interface with direction-dependent surface tension. The central tool is the Cahn–Hoffman transform S(x) = A^(−1/2)x, which maps the Wulff ellipsoid x : x^T A⁻¹x ≤ 1\ to the Euclidean unit ball and converts the anisotropic problem into an equivalent isotropic one with a generalized Robin-type condition on the free boundary. We prove optimal regularity of the solution (C^(1,α) in space and C^(0,α/2) in time up to the free boundary) and C^(1,α)-regularity of the evolving free boundary at non-degenerate points. The parabolic Hausdorff dimension of the space-time singular set is shown to be at most n − 1.Mean curvature flowAnisotropic & nonlocal flowsFree boundary & capillary