{
  "id": "1209.6628",
  "version": "v5",
  "published": "2012-09-28T19:53:33.000Z",
  "updated": "2012-11-16T08:58:15.000Z",
  "title": "Initial value problems for diffusion equations with singular potential",
  "authors": [
    "Konstantinos Gkikas",
    "Laurent Veron"
  ],
  "comment": "To appear in Contemporary Mathematics",
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $V$ be a nonnegative locally bounded function defined in $Q_\\infty:=\\BBR^n\\times(0,\\infty)$. We study under what conditions on $V$ and on a Radon measure $\\gm$ in $\\mathbb{R}^d$ does it exist a function which satisfies $\\partial_t u-\\xD u+ Vu=0$ in $Q_\\infty$ and $u(.,0)=\\xm$. We prove the existence of a subcritical case in which any measure is admissible and a supercritical case where capacitary conditions are needed. We obtain a general representation theorem of positive solutions when $t V(x,t)$ is bounded and we prove the existence of an initial trace in the class of outer regular Borel measures.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2012-11-16T08:58:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "initial value problems",
      "diffusion equations",
      "singular potential",
      "locally bounded function",
      "outer regular borel measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.6628G"
    }
  }
}