{
  "id": "1705.10628",
  "version": "v1",
  "published": "2017-05-28T12:19:14.000Z",
  "updated": "2017-05-28T12:19:14.000Z",
  "title": "Two-phase heat conductors with a stationary isothermic surface and their related elliptic overdetermined problems",
  "authors": [
    "Shigeru Sakaguchi"
  ],
  "comment": "21 pages. arXiv admin note: text overlap with arXiv:1603.04004",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a two-phase heat conductor in two dimensions consisting of a core and a shell with different constant conductivities. When the medium outside the two-phase conductor has a possibly different conductivity, we consider the Cauchy problem in two dimensions where the conductor has temperature 0 and the outside medium has temperature 1. It is shown that, if there is a stationary isothermic surface in the shell near the boundary, then the structure of the conductor must be circular. Moreover, as by-products of the method of the proof, we mention other proofs of all the previous results of the author in $N(\\ge 2)$ dimensions and two theorems on their related two-phase elliptic overdetermined problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-05-28T12:19:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K05",
      "35K10",
      "35B06",
      "35B40",
      "35K15",
      "35K20",
      "35J05",
      "35J25"
    ],
    "keywords": [
      "two-phase heat conductor",
      "stationary isothermic surface",
      "related elliptic overdetermined problems",
      "dimensions",
      "related two-phase elliptic overdetermined problems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}