{
  "id": "1505.04893",
  "version": "v1",
  "published": "2015-05-19T07:15:45.000Z",
  "updated": "2015-05-19T07:15:45.000Z",
  "title": "$L^p$-estimates for parabolic systems with unbounded coefficients coupled at zero and first order",
  "authors": [
    "Luciana Angiuli",
    "Luca Lorenzi",
    "Diego Pallara"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider a class of nonautonomous parabolic first-order coupled systems in the Lebesgue space $L^p({\\mathbb R}^d;{\\mathbb R}^m)$, $(d,m \\ge 1)$ with $p\\in [1,+\\infty)$. Sufficient conditions for the associated evolution operator ${\\bf G}(t,s)$ in $C_b({\\mathbb R}^d;{\\mathbb R}^m)$ to extend to a strongly continuous operator in $L^p({\\mathbb R}^d;{\\mathbb R}^m)$ are given. Some $L^p$-$L^q$ estimates are also established together with $L^p$ gradient estimates.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-05-19T07:15:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35K45",
      "47D06"
    ],
    "keywords": [
      "unbounded coefficients",
      "parabolic systems",
      "first order",
      "nonautonomous parabolic first-order coupled systems",
      "evolution operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150504893A"
    }
  }
}