{
  "id": "2205.09490",
  "version": "v1",
  "published": "2022-05-19T12:00:25.000Z",
  "updated": "2022-05-19T12:00:25.000Z",
  "title": "Operator estimates for non-periodically perforated domains with Dirichlet and nonlinear Robin conditions: strange term",
  "authors": [
    "Denis I. Borisov"
  ],
  "categories": [
    "math.AP",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider a boundary value problem for a general second order linear equation in a domain with an arbitrary fine perforation. The latter is made by small cavities; both the shapes of the cavities and their distribution are arbitrary. The boundaries of the cavities are subject either the Dirichlet or a nonlinear Robin condition. On the perforation, certain rather weak conditions are imposed to ensure that under the homogenization procedure we obtain a similar problem in a non-perforated domain with an additional potential in the equation usually called a strange term. Our main results state the convergence of the solution of the perturbed problem to that of the homogenized one in $W_2^1$- and $L_2$-norms uniformly in $L_2$-norm of the right hand side in the equation. The estimates for the convergence rates are established and their order sharpness is discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-19T12:00:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B27",
      "35B40"
    ],
    "keywords": [
      "nonlinear robin condition",
      "strange term",
      "non-periodically perforated domains",
      "operator estimates",
      "general second order linear equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}