{
  "abstract": "We propose a systematic approach based on trajectories to prove a Poincaré inequality for weak non-negative sub-solutions to hypoelliptic equations with an arbitrary number of Hörmander commutators, both in the local and in the non-local case. As a consequence, we deduce the weak Harnack inequality and Hölder regularity along the line of the De Giorgi method.",
  "abstract_shown": true,
  "affiliations": [
    "Università Politecnica delle Marche, Dipartimento di Ingegneria Industriale e Scienze Matematiche, Via Brecce Bianche 12 60131 Ancona, Italy",
    "Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, F-75006 Paris, France",
    "IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche (Sorbonne Université - IMJ - Case 247 - 4 place Jussieu 75252 Paris cedex 05 / Université Paris Diderot - Bât. Sophie Germain, case 7012 - France)",
    "Université de Montpellier, 499-554 Rue du Truel, 34090 Montpellier, France",
    "University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom",
    "Max Planck Institute for Mathematics in the Sciences, Inselstraße 22, 04103 Leipzig, Germany"
  ],
  "article_type": null,
  "arxiv": "2401.12194",
  "author_total": 6,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Francesca Anceschi",
      "orcid": "0000-0001-7594-3511"
    },
    {
      "affs": [
        1,
        2
      ],
      "name": "Helge Dietert",
      "orcid": "0000-0002-2071-9202"
    },
    {
      "affs": [
        3
      ],
      "name": "Jessica Guerand",
      "orcid": "0000-0001-5616-247X"
    },
    {
      "affs": [
        4
      ],
      "name": "Amélie Loher",
      "orcid": "0000-0001-8836-0403"
    },
    {
      "affs": [
        4
      ],
      "name": "Clément Mouhot",
      "orcid": "0000-0002-4755-5404"
    },
    {
      "affs": [
        5
      ],
      "name": "Annalaura Rebucci",
      "orcid": "0000-0002-0353-9410"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/agek70w9cd9hv.bib",
  "cited_by": 12,
  "doi": "10.5802/jep.350",
  "fulltext_url": null,
  "id": "agek70w9cd9hv",
  "issns": [
    "2429-7100",
    "2270-518X"
  ],
  "landing_url": "https://hal.science/hal-05370944v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "1.math.math-ap"
    ],
    [
      "openalex",
      "2604|Nonlinear Partial Differential Equations"
    ]
  ],
  "openalex": "W4391159130",
  "pdf_url": "https://hal.science/hal-05370944/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": "École polytechnique",
  "ris": "https://research.draconitic.com/paper/agek70w9cd9hv.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:24Z",
      "native_id": "hal-05370944",
      "source": "hal",
      "url": "https://hal.science/hal-05370944v2"
    },
    {
      "first_seen": "2026-11-07T13:20:42Z",
      "native_id": "W4391159130",
      "source": "openalex",
      "url": "https://doi.org/10.5802/jep.350"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-ap",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators",
  "title_text": "Poincaré inequality and quantitative De Giorgi method for hypoelliptic operators",
  "type": "peer-reviewed",
  "updated_at": "2026-11-07T13:20:42Z",
  "url": "https://research.draconitic.com/paper/agek70w9cd9hv",
  "venue": "Journal de l'École polytechnique — Mathématiques",
  "versions": []
}