{
  "titles": [
    {
      "title": "Large field problem in coercive singular PDEs"
    }
  ],
  "creators": [
    {
      "name": "Chevyrev, Ilya",
      "nameType": "Personal",
      "familyName": "Chevyrev",
      "givenName": "Ilya"
    },
    {
      "name": "Gubinelli, Massimiliano",
      "nameType": "Personal",
      "familyName": "Gubinelli",
      "givenName": "Massimiliano"
    }
  ],
  "publisher": {
    "name": "Papers of Massimiliano Gubinelli"
  },
  "publicationYear": 2025,
  "types": {
    "resourceTypeGeneral": "Preprint"
  },
  "version": "2",
  "url": "https://arxiv.org/abs/2510.20716v2",
  "dates": [
    {
      "date": "2025-10-23",
      "dateType": "Issued"
    },
    {
      "date": "2025-12-12",
      "dateType": "Available"
    }
  ],
  "language": "en",
  "formats": [
    "application/pdf",
    "application/x-tex"
  ],
  "subjects": [
    {
      "subject": "math.AP",
      "subjectScheme": "arXiv"
    },
    {
      "subject": "math.PR",
      "subjectScheme": "arXiv"
    }
  ],
  "rightsList": [
    {
      "rights": "Creative Commons Attribution 4.0 International",
      "rightsIdentifier": "cc-by-4.0",
      "rightsUri": "http://creativecommons.org/licenses/by/4.0/",
      "rightsIdentifierScheme": "SPDX"
    }
  ],
  "descriptions": [
    {
      "description": "We derive a priori estimates for singular differential equations of the form $\\mathcal{L} \\phi = P(\\phi,\\nabla\\phi) + f(\\phi,\\nabla\\phi)\\xi$ where $P$ is a polynomial, $f$ is a sufficiently well-behaved function, and $\\xi$ is an irregular distribution such that the equation is subcritical. The differential operator $\\mathcal L$ is either a derivative in time, in which case we interpret the equation using rough path theory, or a heat operator, in which case we interpret the equation using regularity structures. Our only assumption on $P$ is that solutions with $\\xi=0$ exhibit coercivity. Our estimates are local in space and time, and independent of boundary conditions.\nOne of our main results is an abstract estimate that allows one to pass from a local coercivity property to a global one using scaling, for a large class of equations. This allows us to reduce the problem of deriving a priori estimates to the case when $\\xi$ is small.",
      "descriptionType": "Abstract"
    }
  ],
  "relatedIdentifiers": [
    {
      "relatedIdentifier": "arXiv:2510.20716v2",
      "relatedIdentifierType": "arXiv",
      "relationType": "IsIdenticalTo"
    },
    {
      "relatedIdentifier": "10.48550/arXiv.2510.20716",
      "relatedIdentifierType": "DOI",
      "relationType": "IsVersionOf"
    }
  ]
}