{
  "id": "2310.10866",
  "version": "v1",
  "published": "2023-10-16T22:26:21.000Z",
  "updated": "2023-10-16T22:26:21.000Z",
  "title": "The linear elasticity system under singular forces",
  "authors": [
    "Alejandro Allendes",
    "Gilberto Campaña",
    "Enrique Otárola",
    "Abner J. Salgado"
  ],
  "categories": [
    "math.NA",
    "cs.NA"
  ],
  "abstract": "We study the linear elasticity system subject to singular forces. We show existence and uniqueness of solutions in two frameworks: weighted Sobolev spaces, where the weight belongs to the Muckenhoupt class $A_2$; and standard Sobolev spaces where the integrability index is less than $d/(d-1)$; $d$ is the spatial dimension. We propose a standard finite element scheme and provide optimal error estimates in the $\\mathbf{L}^2$--norm. By proving well posedness, we clarify some issues concerning the study of generalized mixed problems in Banach spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-10-16T22:26:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R06",
      "65N12",
      "65N15",
      "74S05"
    ],
    "keywords": [
      "singular forces",
      "linear elasticity system subject",
      "standard finite element scheme",
      "standard sobolev spaces",
      "optimal error estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}