{
  "id": "2011.06574",
  "version": "v1",
  "published": "2020-11-12T18:45:48.000Z",
  "updated": "2020-11-12T18:45:48.000Z",
  "title": "Generalized Carleson perturbations of elliptic operators and applications",
  "authors": [
    "Joseph Feneuil",
    "Bruno Poggi"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "We extend in two directions the notion of perturbations of Carleson type for the Dirichlet problem associated to an elliptic real second-order divergence-form (possibly degenerate, not necessarily symmetric) elliptic operator. First, in addition to the classical perturbations of Carleson type, that we call additive Carleson perturbations, we introduce scalar-multiplicative and antisymmetric Carleson perturbations, which both allow non-trivial differences at the boundary. Second, we consider domains which admit an elliptic PDE in a broad sense: we count as examples the 1-sided NTA (a.k.a. uniform) domains satisfying the capacity density condition, the 1-sided chord-arc domains, the domains with low-dimensional Ahlfors-David regular boundaries, and certain domains with mixed-dimensional boundaries; thus our methods provide a unified perspective on the Carleson perturbation theory of elliptic operators. Our proofs do not introduce sawtooth domains or the extrapolation method. We also present several applications to some Dahlberg-Kenig-Pipher operators, free-boundary problems, and we provide a new characterization of $A_{\\infty}$ among elliptic measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-12T18:45:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic operator",
      "generalized carleson perturbations",
      "applications",
      "elliptic real second-order divergence-form",
      "low-dimensional ahlfors-david regular boundaries"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}