{
  "id": "1511.05912",
  "version": "v1",
  "published": "2015-11-18T19:05:16.000Z",
  "updated": "2015-11-18T19:05:16.000Z",
  "title": "On G-convergence of positive Self-adjoint operators",
  "authors": [
    "Hasan Almanasreh",
    "Mahmoud Shalalfeh"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We apply G-convergence theory to study the asymptotic of the eigenvalue problems of positive definite bounded self-adjoint $h$-dependent operators as $h\\to\\infty$. Two operators are considered; a second order elliptic operator and a general linear operator. Using the definition of G-convergence of elliptic operator, we review convergence results of the elliptic eigenvalue problem as $h\\to\\infty$. Also employing the general definition of G-convergence of positive definite self-adjoint operator together with $\\Gamma$-convergence of the associated quadratic form, we characterize the G-limit as $h\\to\\infty$ of the general operator with some classes of perturbations. As a consequence, we also prove the convergence of the corresponding spectrum.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-18T19:05:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "positive self-adjoint operators",
      "g-convergence",
      "second order elliptic operator",
      "review convergence results",
      "positive definite self-adjoint operator"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151105912A"
    }
  }
}