{
  "abstract": "This paper studies a Chambolle-type minimizing movement scheme for mean curvature flow with prescribed contact angle in a smooth bounded domain. The scheme is based on the capillary functional and the geodesic signed distance relative to the container, and yields a time-discrete level-set approximation. The main result asserts that, for every Lipschitz-continuous boundary function prescribing a strictly nondegenerate contact angle, the approximate solutions converge locally uniformly to the unique viscosity solution of the corresponding level-set mean curvature equation with oblique derivative boundary condition. This improves a previous convergence theorem, where the container was assumed to be convex and a curvature-type condition relating the tangential derivative of the prescribed contact-angle function to the principal curvatures of the container boundary was imposed. The main new ingredient is a uniform Lipschitz estimate for the solutions of the variational problems defining the scheme. This estimate is derived by applying a Bernstein-type argument to a suitable weighted gradient, rather than to the gradient itself, which rules out boundary maxima without relying on the previous curvature-type condition.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.00094",
  "author_total": 2,
  "authors": [
    {
      "name": "Tokuhiro Eto"
    },
    {
      "name": "Jiwoong Jang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5e0q7mrqr5732.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.00094",
  "fulltext_url": null,
  "id": "5e0q7mrqr5732",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.00094",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AP"
    ],
    [
      "openalex",
      "2604|Geometric Analysis and Curvature Flows"
    ]
  ],
  "openalex": "W7167012853",
  "pdf_url": "https://arxiv.org/pdf/2607.00094",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5e0q7mrqr5732.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2607.00094",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.00094"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Convergence of a minimizing movement scheme for contact-angle mean curvature flow in a smooth bounded domain",
  "title_text": "Convergence of a minimizing movement scheme for contact-angle mean curvature flow in a smooth bounded domain",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/5e0q7mrqr5732",
  "venue": "arXiv",
  "versions": []
}