{
  "id": "2106.04702",
  "version": "v1",
  "published": "2021-06-08T21:33:53.000Z",
  "updated": "2021-06-08T21:33:53.000Z",
  "title": "Existence, comparison, and convergence results for a class of elliptic hemivariational inequalities",
  "authors": [
    "Claudia M. Gariboldi",
    "Stanisław Migórski",
    "Anna Ochal",
    "Domingo A. Tarzia"
  ],
  "comment": "22 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study a class of elliptic boundary hemivariational inequalities which originates in the steady-state heat conduction problem with nonmonotone multivalued subdifferential boundary condition on a portion of the boundary described by the Clarke generalized gradient of a locally Lipschitz function. First, we prove a new existence result for the inequality employing the theory of pseudomonotone operators. Next, we give a result on comparison of solutions, and provide sufficient conditions that guarantee the asymptotic behavior of solution, when the heat transfer coefficient tends to infinity. Further, we show a result on the continuous dependence of solution on the internal energy and heat flux. Finally, some examples of convex and nonconvex potentials illustrate our hypotheses.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-06-08T21:33:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J05",
      "35J65",
      "35J87",
      "49J45"
    ],
    "keywords": [
      "inequality",
      "elliptic hemivariational inequalities",
      "convergence results",
      "comparison",
      "elliptic boundary hemivariational inequalities"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}