{
  "id": "2007.08462",
  "version": "v1",
  "published": "2020-07-16T17:00:34.000Z",
  "updated": "2020-07-16T17:00:34.000Z",
  "title": "Existence and improved regularity for a nonlinear system with collapsing ellipticity",
  "authors": [
    "Edgard A. Pimentel",
    "José Miguel Urbano"
  ],
  "comment": "Manuscript accepted for publication in Ann. Sc. Norm. Super. Pisa Cl. Sci",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study a nonlinear system made up of an elliptic equation of blended singular/degenerate type and Poisson's equation with a lowly integrable source. We prove the existence of a weak solution in any space dimension and, chiefly, derive an improved $\\mathcal{C}^{1,\\text{log-Lip}}$-regularity estimate using tangential analysis methods. The system illustrates a sophisticated version of the proverbial thermistor problem and our results are new even in simpler modelling scenarios.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-16T17:00:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear system",
      "collapsing ellipticity",
      "tangential analysis methods",
      "proverbial thermistor problem",
      "blended singular/degenerate type"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}