{
  "id": "2301.11677",
  "version": "v1",
  "published": "2023-01-27T12:19:32.000Z",
  "updated": "2023-01-27T12:19:32.000Z",
  "title": "Strong unique continuation from the boundary for the spectral fractional Laplacian",
  "authors": [
    "Alessandra De Luca",
    "Veronica Felli",
    "Giovanni Siclari"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We investigate unique continuation properties and asymptotic behaviour at boundary points for solutions to a class of elliptic equations involving the spectral fractional Laplacian. An extension procedure leads us to study a degenerate or singular equation on a cylinder, with a homogeneous Dirichlet boundary condition on the lateral surface and a non homogeneous Neumann condition on the basis. For the extended problem, by an Almgren-type monotonicity formula and a blow-up analysis, we classify the local asymptotic profiles at the edge where the transition between boundary conditions occurs. Passing to traces, an analogous blow-up result and its consequent strong unique continuation property is deduced for the nonlocal fractional equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-01-27T12:19:32.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R11",
      "35B40",
      "31B25"
    ],
    "keywords": [
      "spectral fractional laplacian",
      "consequent strong unique continuation property",
      "nonlocal fractional equation",
      "boundary conditions occurs",
      "local asymptotic profiles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}