{
  "id": "0903.5482",
  "version": "v1",
  "published": "2009-03-31T14:22:43.000Z",
  "updated": "2009-03-31T14:22:43.000Z",
  "title": "Flows and invariance for elliptic operators",
  "authors": [
    "A. F. M. ter Elst",
    "Derek W. Robinson",
    "Adam Sikora"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Let $S$ be the submarkovian semigroup on $L_2({\\bf R}^d)$ generated by a self-adjoint, second-order, divergence-form, elliptic operator $H$ with $W^{1,\\infty}$ coefficients $c_{kl}$. Further let $\\Omega$ be an open subset of ${\\bf R}^d$. Under mild conditions we prove that $S$ leaves $L_2(\\Omega)$ invariant if, and only if, it is invariant under the flows generated by the vector fields $\\sum_{l=1}^d c_{kl} \\partial_l$ for all $k$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-03-31T14:22:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70"
    ],
    "keywords": [
      "elliptic operator",
      "invariance",
      "submarkovian semigroup",
      "open subset",
      "mild conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.5482T"
    }
  }
}