{
  "id": "1903.11224",
  "version": "v1",
  "published": "2019-03-27T02:08:40.000Z",
  "updated": "2019-03-27T02:08:40.000Z",
  "title": "Existence and Regularity of Weak Solutions to a Thermoelectric Model",
  "authors": [
    "Xing-Bin Pan",
    "Zhibing Zhang"
  ],
  "comment": "provisionally accepted by Nonlinearity",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of the equations, and with the help of the De Giorgi-Nash estimate for elliptic equations, we obtain existence of weak solutions on Lipschitz domains for general boundary data. Using Campanato's method, we establish regularity results of the weak solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-03-27T02:08:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "weak solutions",
      "elliptic equation",
      "general boundary data",
      "time-independent thermoelectric model",
      "boundary conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}