{
  "id": "2408.12529",
  "version": "v1",
  "published": "2024-08-22T16:32:55.000Z",
  "updated": "2024-08-22T16:32:55.000Z",
  "title": "Perturbation theory for the parabolic regularity problem",
  "authors": [
    "Martin Ulmer"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We show small and large Carleson perturbation results for the parabolic regularity boundary value problem with boundary data in $\\dot{L}_{1,1/2}^p$. The operator we consider is $L:=\\partial_t -\\mathrm{div}(A\\nabla\\cdot)$ and the domains are parabolic cylinders $\\Omega=\\mathcal{O}\\times\\mathbb{R}$, where $\\mathcal{O}$ is a chord arc domain or Lipschitz domain.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-22T16:32:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K10",
      "35K20"
    ],
    "keywords": [
      "parabolic regularity problem",
      "perturbation theory",
      "parabolic regularity boundary value problem",
      "large carleson perturbation results",
      "chord arc domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}