{
  "id": "1711.01389",
  "version": "v1",
  "published": "2017-11-04T03:38:16.000Z",
  "updated": "2017-11-04T03:38:16.000Z",
  "title": "Partial continuity for nonlinear systems with nonstandard growth and discontinuous coefficients",
  "authors": [
    "Chris van der Heide"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain new partial H\\\"older continuity results for solutions to divergence form elliptic systems with discontinuous coefficients, obeying $p(x)$-type nonstandard growth conditions. By an application of the method of $\\mathcal{A}$-harmonic approximation, we are able to allow for both VMO-discontinuities in the coefficients, and the minimal $\\log$-H\\\"older regularity assumption on the exponent function. In doing so, we recover a local version of the quantisation phenomenon characteristic continuous coefficient case.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-04T03:38:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B65",
      "35J47"
    ],
    "keywords": [
      "discontinuous coefficients",
      "nonlinear systems",
      "partial continuity",
      "phenomenon characteristic continuous coefficient case",
      "quantisation phenomenon characteristic continuous coefficient"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}