{
  "id": "0805.4550",
  "version": "v1",
  "published": "2008-05-29T14:05:44.000Z",
  "updated": "2008-05-29T14:05:44.000Z",
  "title": "Optimal conditions for $L^\\infty$-regularity and a priori estimates for elliptic systems, I: two components",
  "authors": [
    "Li Yuxiang"
  ],
  "comment": "21pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we present a new bootstrap procedure for elliptic systems with two unknown functions. Combining with the $L^p$-$L^q$-estimates, it yields the optimal $L^\\infty$-regularity conditions for the three well-known types of weak solutions: $H_0^1$-solutions, $L^1$-solutions and $L^1_\\delta$-solutions. Thanks to the linear theory in $L^p_\\delta(\\Omega)$, it also yields the optimal conditions for a priori estimates for $L^1_\\delta$-solutions. Based on the a priori estimates, we improve known existence theorems for some classes of elliptic systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-05-29T14:05:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J25",
      "35J55",
      "35J60",
      "35B45"
    ],
    "keywords": [
      "elliptic systems",
      "priori estimates",
      "optimal conditions",
      "components",
      "existence theorems"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0805.4550Y"
    }
  }
}