{
  "id": "2103.04665",
  "version": "v1",
  "published": "2021-03-08T11:03:47.000Z",
  "updated": "2021-03-08T11:03:47.000Z",
  "title": "Strong unique continuation and local asymptotics at the boundary for fractional elliptic equations",
  "authors": [
    "Alessandra De Luca",
    "Veronica Felli",
    "Stefano Vita"
  ],
  "comment": "40 pages, 2 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study local asymptotics of solutions to fractional elliptic equations at boundary points, under some outer homogeneous Dirichlet boundary condition. Our analysis is based on a blow-up procedure which involves some Almgren type monotonicity formulae and provides a classification of all possible homogeneity degrees of limiting entire profiles. As a consequence, we establish a strong unique continuation principle from boundary points.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-08T11:03:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31B25",
      "35R11",
      "35C20"
    ],
    "keywords": [
      "fractional elliptic equations",
      "local asymptotics",
      "outer homogeneous dirichlet boundary condition",
      "boundary points",
      "almgren type monotonicity formulae"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}