{
  "abstract": "We prove the Lipschitz regularity of solutions for a wide class of generalized Bernoulli free boundary problems, in vectorial, higher order, and non-minimizing settings. Our method does not rely on notions of viscosity solutions or comparison methods, which allows us to reach the optimal regularity for Bernoulli-type problems associated to elliptic operators which do not satisfy any maximum principle, namely the elasticity, biharmonic and Stokes equation. With a similar method we obtain the optimal Lipschitz regularity for stationary, non-minimizing solutions of the standard Bernoulli problem in two dimensions.",
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  "arxiv": "2609.12180",
  "author_total": 3,
  "authors": [
    {
      "name": "Guido De Philippis"
    },
    {
      "name": "Jonas Hirsch"
    },
    {
      "name": "Mickaël Nahon"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ca8jhjc5ymf4a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12180",
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  "id": "ca8jhjc5ymf4a",
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  "landing_url": "https://hal.science/hal-05746140v2",
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  "pdf_url": "https://hal.science/hal-05746140/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ca8jhjc5ymf4a.ris",
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      "first_seen": "2026-10-30T12:17:42Z",
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      "url": "https://arxiv.org/abs/2609.12180"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
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  "title": "Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems",
  "title_text": "Optimal regularity for vectorial, higher order and non-minimizing Bernoulli problems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:35Z",
  "url": "https://research.draconitic.com/paper/ca8jhjc5ymf4a",
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